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1. Shard Calculation

Query:

Response:

Calculated Shard: 122 (from laksa132)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa122.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://www.merriam-webster.com/dictionary/Laplace%20transform\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.merriam-webster.com/dictionary/Laplace%20transform\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform","crawl_time":1774567530,"first_indexed_time":1481840549,"http_code":200,"src_unparsed":"com,merriam-webster!www,\/dictionary\/Laplace%20transform s443","src_root_hash":"12021194709005532322","history_drop_reason":null,"meta_title":"LAPLACE TRANSFORM Definition & Meaning - Merriam-Webster","meta_descriptions":["The meaning of LAPLACE TRANSFORM is a transformation of a function f(x) into the function ... that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation."],"attrs_boilerpipe_text":":\na transformation of a\nfunction\nf\n(\nx\n) into the function\ng\n(\nt\n)\n=\n∫\no\n∞\ne\n−\nx\nt\nf\n(\nx\n)\nd\nx\nthat is useful especially in reducing the solution of an ordinary linear\ndifferential equation\nwith constant coefficients to the solution of a polynomial equation\nWord History\nEtymology\nPierre Simon, Marquis de\nlaplace\nFirst Known Use\n1942, in the meaning defined\nabove\nTime Traveler\nThe first known use of\nLaplace transform\nwas\n                                        in 1942\nBrowse Nearby Words\nCite this Entry\nStyle\n“Laplace transform.”\nMerriam-Webster.com Dictionary\n, Merriam-Webster, https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform. Accessed 26 Mar. 2026.\nMore from Merriam-Webster on\nLaplace transform\nLove words? Need even more definitions?\nSubscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!\nMerriam-Webster unabridged\nMore from Merriam-Webster\nTop Lookups","attrs_markdown":"[Chatbot](https:\/\/www.merriam-webster.com\/chatbot)\n\n- [Chatbot](https:\/\/www.merriam-webster.com\/chatbot)\n- [Games](https:\/\/www.merriam-webster.com\/games)\n- [Word of the Day](https:\/\/www.merriam-webster.com\/word-of-the-day)\n- [Grammar](https:\/\/www.merriam-webster.com\/grammar)\n- [Word Finder](https:\/\/www.merriam-webster.com\/wordfinder)\n- [Slang](https:\/\/www.merriam-webster.com\/slang)\n- New [Newsletters](https:\/\/www.merriam-webster.com\/newsletters)\n- [Wordplay](https:\/\/www.merriam-webster.com\/wordplay)\n- [Rhymes](https:\/\/www.merriam-webster.com\/rhymes)\n- [Thesaurus](https:\/\/www.merriam-webster.com\/thesaurus)\n- [Join MWU](https:\/\/unabridged.merriam-webster.com\/check-redirect-premium?utm_source=mw&utm_medium=global-nav-join&utm_campaign=evergreen)\n- More\n  - 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[My Words](https:\/\/www.merriam-webster.com\/saved-words)\n    - [Recents](https:\/\/www.merriam-webster.com\/recents)\n    - [Account](https:\/\/www.merriam-webster.com\/settings)\n    - [Log Out](https:\/\/www.merriam-webster.com\/logout)\n\nEst. 1828\n\n[Dictionary](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform)\n\n- [![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/sidebar-nav-item-icon.svg) Definition](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#dictionary-entry-1)\n- [![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/sidebar-nav-item-icon.svg) Definition](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#dictionary-entry-1)\n- [![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/sidebar-nav-item-icon.svg) Word History](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#word-history)\n- [![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/sidebar-nav-item-icon.svg) Rhymes](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#related-rhymes)\n- [![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/sidebar-nav-item-icon.svg) Entries Near](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#nearby-entries)\n\n- - [![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/sidebar-nav-item-icon.svg) Cite this EntryCitation](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#citations)\n  - [![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/sidebar-nav-item-icon.svg) More from M-W](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#more-from-mw)\n  [![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/redesign\/dots.svg) Show more![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/redesign\/show-more-arrow.svg)](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform)\n- [More from M-W![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/redesign\/show-more-arrow.svg)](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform)\n  - [Citation](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#citations)\n  - [More from M-W](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#more-from-mw)\n\n- Save Word ![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/redesign\/save-word-flag-icon.svg)\n  - To save this word, you'll need to log in.\n    [Log In](https:\/\/www.merriam-webster.com\/login)\n\n# Laplace transform\n## [noun](https:\/\/www.merriam-webster.com\/dictionary\/noun)\n\nLa·place transform\n\n[lə-ˈpläs-](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform?pronunciation&lang=en_us&dir=l&file=laplac02 \"How to pronounce Laplace transform (audio)\")\n\n[\\-ˈplas-](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform?pronunciation&lang=en_us&dir=l&file=laplac01 \"How to pronounce Laplace transform (audio)\")\n\n**:** a transformation of a [function](https:\/\/www.merriam-webster.com\/dictionary\/function#h1) *f*(*x*) into the function\n\ng(t)\\=∫∞oe−xtf(x)dx\n\ng\n\n(\n\nt\n\n)\n\n\\=\n\n∫\n\no\n\n∞\n\ne\n\n−\n\nx\n\nt\n\nf\n\n(\n\nx\n\n)\n\nd\n\nx\n\nthat is useful especially in reducing the solution of an ordinary linear [differential equation](https:\/\/www.merriam-webster.com\/dictionary\/differential%20equation) with constant coefficients to the solution of a polynomial equation\n\n## Word History\nEtymology\n\nPierre Simon, Marquis de [laplace](https:\/\/www.merriam-webster.com\/dictionary\/Laplace#b)\n\nFirst Known Use\n\n1942, in the meaning defined [above](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#h1)\n\nTime Traveler\n\nThe first known use of *Laplace transform* was in 1942\n\n[See more words from the same year](https:\/\/www.merriam-webster.com\/time-traveler\/1942?src=defrecirc-timetraveler-etycard)\n\n## Rhymes for *Laplace transform*\n- [epileptiform](https:\/\/www.merriam-webster.com\/dictionary\/epileptiform)\n- [hydatidiform](https:\/\/www.merriam-webster.com\/dictionary\/hydatidiform)\n- [brainstorm](https:\/\/www.merriam-webster.com\/dictionary\/brainstorm)\n- [conform](https:\/\/www.merriam-webster.com\/dictionary\/conform)\n- [deform](https:\/\/www.merriam-webster.com\/dictionary\/deform)\n- [firestorm](https:\/\/www.merriam-webster.com\/dictionary\/firestorm)\n- [hailstorm](https:\/\/www.merriam-webster.com\/dictionary\/hailstorm)\n- [inform](https:\/\/www.merriam-webster.com\/dictionary\/inform)\n- [landform](https:\/\/www.merriam-webster.com\/dictionary\/landform)\n- [lukewarm](https:\/\/www.merriam-webster.com\/dictionary\/lukewarm)\n- [perform](https:\/\/www.merriam-webster.com\/dictionary\/perform)\n- [planform](https:\/\/www.merriam-webster.com\/dictionary\/planform)\n\n[See All Rhymes for *Laplace transform*](https:\/\/www.merriam-webster.com\/rhymes\/perfect\/laplace%20transform)\n\n## Browse Nearby Words\n[Laplace station](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20station)\n\nLaplace transform\n\n[Laplacian](https:\/\/www.merriam-webster.com\/dictionary\/Laplacian)\n\n[See all Nearby Words](https:\/\/www.merriam-webster.com\/browse\/dictionary\/l\/6)\n\n## Cite this Entry\nStyle\n\n“Laplace transform.” *Merriam-Webster.com Dictionary*, Merriam-Webster, https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform. Accessed 26 Mar. 2026.\n\n[![](https:\/\/www.merriam-webster.com\/dist-cross-dungarees\/2026-03-26--19-00-45-isc4p\/images\/svg\/redesign\/copy-icon.svg)Copy Citation](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform)\n\n## More from Merriam-Webster on *Laplace transform*\nBritannica.com: [Encyclopedia article about *Laplace transform*](https:\/\/www.britannica.com\/EBchecked\/topic\/330345\/Laplace-transform)\n\nLove words? Need even more definitions?\n\nSubscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free\\!\n\n[Merriam-Webster unabridged](https:\/\/unabridged.merriam-webster.com\/check-redirect-premium?utm_source=mw&utm_medium=inline-def&utm_campaign=evergreen&headword=Laplace%20transform)\n\n## More from Merriam-Webster\nTop Lookups\n\n- 1\n  existential\n- 2\n  happy\n- 3\n  enigma\n- 4\n  culture\n- 5\n  didactic\n- 6\n  pedantic\n- 7\n  love\n\n#### [Word of the Day](https:\/\/www.merriam-webster.com\/word-of-the-day)\n#### [zany](https:\/\/www.merriam-webster.com\/word-of-the-day)\n[See Definitions and Examples](https:\/\/www.merriam-webster.com\/word-of-the-day) »\n\nGet Word of the Day daily email\\!\n\n## Popular in Grammar & Usage\n[See More](https:\/\/www.merriam-webster.com\/grammar)\n\n[Are You Misusing These 10 Common Words?](https:\/\/www.merriam-webster.com\/grammar\/words-that-do-not-mean-what-you-think-they-mean)\n\n[5 Verbal Slip Ups and Language Mistakes](https:\/\/www.merriam-webster.com\/grammar\/mondegreens-eggcorns-malapropisms-spoonerism-freudian-slip)\n\n[Is that lie 'bald-faced' or 'bold-faced'?](https:\/\/www.merriam-webster.com\/grammar\/is-that-lie-bald-faced-or-bold-faced-or-barefaced)\n\n[The Difference Between 'i.e.' and 'e.g.'](https:\/\/www.merriam-webster.com\/grammar\/ie-vs-eg-abbreviation-meaning-usage-difference)\n\n[Why is '-ed' sometimes pronounced at the end of a word?](https:\/\/www.merriam-webster.com\/grammar\/why-do-we-pronounce-ed-at-the-end-of-a-word)\n\n[See More](https:\/\/www.merriam-webster.com\/grammar)\n\n## Popular in Wordplay\n[See More](https:\/\/www.merriam-webster.com\/wordplay)\n\n[12 Words for Signs of Spring](https:\/\/www.merriam-webster.com\/wordplay\/signs-of-spring)\n\n[The Opposite of Déjà Vu](https:\/\/www.merriam-webster.com\/wordplay\/the-opposite-of-deja-vu)\n\n[Why do we call it a 'pipe dream'?](https:\/\/www.merriam-webster.com\/wordplay\/why-do-we-call-it-a-pipe-dream)\n\n[Why do we say 'fly off the handle'?](https:\/\/www.merriam-webster.com\/wordplay\/why-do-we-say-fly-off-the-handle)\n\n[Why do we call it a 'flea market'?](https:\/\/www.merriam-webster.com\/wordplay\/why-do-we-call-it-a-flea-market)\n\n[See More](https:\/\/www.merriam-webster.com\/wordplay)\n\n## Popular\n[See More](https:\/\/www.merriam-webster.com\/wordplay)\n\n[Are You Misusing These 10 Common Words?](https:\/\/www.merriam-webster.com\/grammar\/words-that-do-not-mean-what-you-think-they-mean)\n\n[12 Words for Signs of Spring](https:\/\/www.merriam-webster.com\/wordplay\/signs-of-spring)\n\n[The Opposite of Déjà Vu](https:\/\/www.merriam-webster.com\/wordplay\/the-opposite-of-deja-vu)\n\n[See More](https:\/\/www.merriam-webster.com\/wordplay)\n\n## Games & Quizzes\n[See All](https:\/\/www.merriam-webster.com\/games)\n\n[![Play Quordle: Guess all four words in a limited number of tries. Each of your guesses must be a real 5-letter word.](https:\/\/merriam-webster.com\/assets\/mw\/static\/images\/games\/external\/quordle\/485x364@1x.jpg) Quordle Can you solve 4 words at once? Play](https:\/\/www.merriam-webster.com\/games\/quordle\/)\n\n[![Play Blossom: Solve today's spelling word game by finding as many words as you can using just 7 letters. Longer words score more points.](https:\/\/merriam-webster.com\/assets\/mw\/static\/images\/games\/iframe\/blossom-word-game\/485x364@1x.jpg) Blossom Pick the best words! Play](https:\/\/www.merriam-webster.com\/games\/blossom-word-game)\n\n[![Play Missing Letter: a crossword with a twist. Each of the 25 puzzle words start with a different letter of the alphabet. Which letter is missing?](https:\/\/merriam-webster.com\/assets\/mw\/static\/images\/games\/iframe\/missing-letter\/485x364@1x.jpg) The Missing Letter A daily crossword with a twist Play](https:\/\/www.merriam-webster.com\/games\/missing-letter)\n\n[![back-of-head-mortarboard](https:\/\/merriam-webster.com\/assets\/mw\/images\/quiz\/quiz-global-footer-recirc\/back-of-head-mortarboard-10064-e628383268d81f98a3a47ca0f9d93478@1x.jpg) Quiz: Name That Hat! Time to put on your thinking cap. Take the quiz](https:\/\/www.merriam-webster.com\/games\/name-that-hat)\n\n[See All](https:\/\/www.merriam-webster.com\/games)\n\n[Merriam Webster](https:\/\/www.merriam-webster.com\/)\n\nLearn a new word every day. Delivered to your inbox\\!\n\n- [Help](https:\/\/www.merriam-webster.com\/help)\n- [About Us](https:\/\/www.merriam-webster.com\/about-us)\n- [Advertising Info](https:\/\/corporate.britannica.com\/advertise-with-us)\n- [Contact Us](https:\/\/www.merriam-webster.com\/contact-us)\n- [Privacy Policy](https:\/\/www.merriam-webster.com\/privacy-policy)\n- [Terms of Use](https:\/\/www.merriam-webster.com\/terms-of-use)\n\n- [Facebook](https:\/\/www.facebook.com\/merriamwebster)\n- [Twitter](https:\/\/twitter.com\/merriamwebster)\n- [YouTube](https:\/\/www.youtube.com\/user\/MerriamWebsterOnline)\n- [Instagram](https:\/\/www.instagram.com\/merriamwebster\/)\n\n© 2026 Merriam-Webster, Incorporated","attrs_readable_markdown":"**:** a transformation of a [function](https:\/\/www.merriam-webster.com\/dictionary\/function#h1) *f*(*x*) into the function g ( t ) \\= ∫ o ∞ e − x t f ( x ) d x that is useful especially in reducing the solution of an ordinary linear [differential equation](https:\/\/www.merriam-webster.com\/dictionary\/differential%20equation) with constant coefficients to the solution of a polynomial equation\n\nWord History\n\nEtymology\n\nPierre Simon, Marquis de [laplace](https:\/\/www.merriam-webster.com\/dictionary\/Laplace#b)\n\nFirst Known Use\n\n1942, in the meaning defined [above](https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform#h1)\n\nTime Traveler\n\nThe first known use of *Laplace transform* was in 1942\n\nBrowse Nearby Words\n\nCite this Entry\n\nStyle\n\n“Laplace transform.” *Merriam-Webster.com Dictionary*, Merriam-Webster, https:\/\/www.merriam-webster.com\/dictionary\/Laplace%20transform. Accessed 26 Mar. 2026.\n\nMore from Merriam-Webster on *Laplace transform*\n\nLove words? Need even more definitions?\n\nSubscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free\\!\n\n[Merriam-Webster unabridged](https:\/\/unabridged.merriam-webster.com\/check-redirect-premium?utm_source=mw&utm_medium=inline-def&utm_campaign=evergreen&headword=Laplace%20transform)\n\nMore from Merriam-Webster\n\nTop Lookups","meta_canonical":null}

3. Robots.txt Check

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4. Spam/Ban Check

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5. Seen Status Check

ℹ️ Skipped - page is already crawled

📄

INDEXABLE

✅

CRAWLED

20 days ago

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ROBOTS ALLOWED

Page Info Filters

Filter	Status	Condition	Details
HTTP status	PASS	`download_http_code = 200`	HTTP 200
Age cutoff	PASS	`download_stamp > now() - 6 MONTH`	0.7 months ago
History drop	PASS	`isNull(history_drop_reason)`	No drop reason
Spam/ban	PASS	`fh_dont_index != 1 AND ml_spam_score = 0`	ml_spam_score=0
Canonical	PASS	`meta_canonical IS NULL OR = '' OR = src_unparsed`	Not set

Page Details

Property	Value
URL	https://www.merriam-webster.com/dictionary/Laplace%20transform
Last Crawled	2026-03-26 23:25:30 (20 days ago)
First Indexed	2016-12-15 22:22:29 (9 years ago)
HTTP Status Code	200
Meta Title	LAPLACE TRANSFORM Definition & Meaning - Merriam-Webster
Meta Description	The meaning of LAPLACE TRANSFORM is a transformation of a function f(x) into the function ... that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation.
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Boilerpipe Text	: a transformation of a function f ( x ) into the function g ( t ) = ∫ o ∞ e − x t f ( x ) d x that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation Word History Etymology Pierre Simon, Marquis de laplace First Known Use 1942, in the meaning defined above Time Traveler The first known use of Laplace transform was in 1942 Browse Nearby Words Cite this Entry Style “Laplace transform.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/Laplace%20transform. Accessed 26 Mar. 2026. More from Merriam-Webster on Laplace transform Love words? Need even more definitions? Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free! Merriam-Webster unabridged More from Merriam-Webster Top Lookups
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[Log In](https://www.merriam-webster.com/login) # Laplace transform ## [noun](https://www.merriam-webster.com/dictionary/noun) La·place transform [lə-ˈpläs-](https://www.merriam-webster.com/dictionary/Laplace%20transform?pronunciation&lang=en_us&dir=l&file=laplac02 "How to pronounce Laplace transform (audio)") [\-ˈplas-](https://www.merriam-webster.com/dictionary/Laplace%20transform?pronunciation&lang=en_us&dir=l&file=laplac01 "How to pronounce Laplace transform (audio)") : a transformation of a [function](https://www.merriam-webster.com/dictionary/function#h1) f(x) into the function g(t)\=∫∞oe−xtf(x)dx g ( t ) \= ∫ o ∞ e − x t f ( x ) d x that is useful especially in reducing the solution of an ordinary linear [differential equation](https://www.merriam-webster.com/dictionary/differential%20equation) with constant coefficients to the solution of a polynomial equation ## Word History Etymology Pierre Simon, Marquis de [laplace](https://www.merriam-webster.com/dictionary/Laplace#b) First Known Use 1942, in the meaning defined [above](https://www.merriam-webster.com/dictionary/Laplace%20transform#h1) Time Traveler The first known use of Laplace transform was in 1942 [See more words from the same year](https://www.merriam-webster.com/time-traveler/1942?src=defrecirc-timetraveler-etycard) ## Rhymes for Laplace transform - [epileptiform](https://www.merriam-webster.com/dictionary/epileptiform) - [hydatidiform](https://www.merriam-webster.com/dictionary/hydatidiform) - [brainstorm](https://www.merriam-webster.com/dictionary/brainstorm) - [conform](https://www.merriam-webster.com/dictionary/conform) - [deform](https://www.merriam-webster.com/dictionary/deform) - [firestorm](https://www.merriam-webster.com/dictionary/firestorm) - [hailstorm](https://www.merriam-webster.com/dictionary/hailstorm) - [inform](https://www.merriam-webster.com/dictionary/inform) - [landform](https://www.merriam-webster.com/dictionary/landform) - [lukewarm](https://www.merriam-webster.com/dictionary/lukewarm) - [perform](https://www.merriam-webster.com/dictionary/perform) - [planform](https://www.merriam-webster.com/dictionary/planform) [See All Rhymes for Laplace transform](https://www.merriam-webster.com/rhymes/perfect/laplace%20transform) ## Browse Nearby Words [Laplace station](https://www.merriam-webster.com/dictionary/Laplace%20station) Laplace transform [Laplacian](https://www.merriam-webster.com/dictionary/Laplacian) [See all Nearby Words](https://www.merriam-webster.com/browse/dictionary/l/6) ## Cite this Entry Style “Laplace transform.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/Laplace%20transform. Accessed 26 Mar. 2026. [![](https://www.merriam-webster.com/dist-cross-dungarees/2026-03-26--19-00-45-isc4p/images/svg/redesign/copy-icon.svg)Copy Citation](https://www.merriam-webster.com/dictionary/Laplace%20transform) ## More from Merriam-Webster on Laplace transform Britannica.com: [Encyclopedia article about Laplace transform](https://www.britannica.com/EBchecked/topic/330345/Laplace-transform) Love words? Need even more definitions? Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free\! 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Readable Markdown	: a transformation of a [function](https://www.merriam-webster.com/dictionary/function#h1) f(x) into the function g ( t ) \= ∫ o ∞ e − x t f ( x ) d x that is useful especially in reducing the solution of an ordinary linear [differential equation](https://www.merriam-webster.com/dictionary/differential%20equation) with constant coefficients to the solution of a polynomial equation Word History Etymology Pierre Simon, Marquis de [laplace](https://www.merriam-webster.com/dictionary/Laplace#b) First Known Use 1942, in the meaning defined [above](https://www.merriam-webster.com/dictionary/Laplace%20transform#h1) Time Traveler The first known use of Laplace transform was in 1942 Browse Nearby Words Cite this Entry Style “Laplace transform.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/Laplace%20transform. Accessed 26 Mar. 2026. More from Merriam-Webster on Laplace transform Love words? Need even more definitions? Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free\! [Merriam-Webster unabridged](https://unabridged.merriam-webster.com/check-redirect-premium?utm_source=mw&utm_medium=inline-def&utm_campaign=evergreen&headword=Laplace%20transform) More from Merriam-Webster Top Lookups
Shard	122 (laksa)
Root Hash	12021194709005532322
Unparsed URL	com,merriam-webster!www,/dictionary/Laplace%20transform s443