Rule: Q[2, 3, 6, 32]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^{11}-\frac{6923}{164}\cdot t^9+\frac{97479}{164}\cdot t^7-\frac{566685}{164}\cdot t^5+\frac{1313235}{164}\cdot t^3-\frac{418635}{82}\cdot t$
• $P_4$:
  $t^{43}-\frac{777206413554596144125804957212332944481327551817235951123089476858988125821291274138323393}{1056104070806118053678643966725105687591418764603133312724996323351652402389047977350764}\cdot t^{41}+\frac{257748777342921895565304658506533665318135940070984369826513302588340377995361997490047998469}{1056104070806118053678643966725105687591418764603133312724996323351652402389047977350764}\cdot t^{39}-\frac{664150072640571300448298807123810410422859369507395128160284527686468028741294530795170206498275}{13729352920479534697822371567426373938688443939840733065424952203571481231057623705559932}\cdot t^{37}+\frac{87998855371762678816195569241718038156930711467045969969243162733491492400835456698552506786719325}{13729352920479534697822371567426373938688443939840733065424952203571481231057623705559932}\cdot t^{35}-\frac{590027830922071724814884872107452636428617032664301777700572447583504320963725630311050083389451465}{980668065748538192701597969101883852763460281417195218958925157397962945075544550397138}\cdot t^{33}+\frac{20290643762847229349319169281399405989116853273609230666904945461700248842214159447195408048908962535}{490334032874269096350798984550941926381730140708597609479462578698981472537772275198569}\cdot t^{31}-\frac{1043359537503517343845503257635176634318065054425189970341912348558553863043368603800772373393978427305}{490334032874269096350798984550941926381730140708597609479462578698981472537772275198569}\cdot t^{29}+\frac{40578006669938432189917244135968531433121747500567849544445077233479109413660512289049271538749553283925}{490334032874269096350798984550941926381730140708597609479462578698981472537772275198569}\cdot t^{27}-\frac{184641797831597437466388020908090253257706572584657649664846752597999714909573664480950956599178203901525}{75436005057579860977045997623221834827958483185938093766071165953689457313503426953626}\cdot t^{25}+\frac{4155600522008653395520313844784294346578727943538186438557599852802519412205562396187659838122392412388125}{75436005057579860977045997623221834827958483185938093766071165953689457313503426953626}\cdot t^{23}-\frac{70899266573925847782504632878863740947846331197932963744691108422061151924199442328170926654220664793993375}{75436005057579860977045997623221834827958483185938093766071165953689457313503426953626}\cdot t^{21}+\frac{909480971954310413123483631284542115865865735601785674221598315570697697432833131280143269313707329628777625}{75436005057579860977045997623221834827958483185938093766071165953689457313503426953626}\cdot t^{19}-\frac{4328687106980456423427840456564269990496759347725674507153407408909152569278484933506307566688561607026457500}{37718002528789930488522998811610917413979241592969046883035582976844728656751713476813}\cdot t^{17}+\frac{29995764576108099168897808476050643836213770632650497066970305221570521980839185986365847194205383218951724375}{37718002528789930488522998811610917413979241592969046883035582976844728656751713476813}\cdot t^{15}-\frac{147265464134235897899469802423174862504504386477191795965819467297248642697905036033281594623785349831437800625}{37718002528789930488522998811610917413979241592969046883035582976844728656751713476813}\cdot t^{13}+\frac{12027887937582578875408732329197005170190591352392963558113089059870888800015640104262522519095792595521652500}{919951281189998304598121922234412619853152233974854802025258121386456796506139353093}\cdot t^{11}-\frac{4271160003602439426702072053830020150646039718239549876226393880619642772320285304844713293207224019298930814375}{150872010115159721954091995246443669655916966371876187532142331907378914627006853907252}\cdot t^9+\frac{5546006874667759120440300722089546048357060213623786323112067849405795840011417368378899033545017264011419196875}{150872010115159721954091995246443669655916966371876187532142331907378914627006853907252}\cdot t^7-\frac{3883562376215640774853717333279210845616952494215340612311734187169969548858850228140290179216872338380026440625}{150872010115159721954091995246443669655916966371876187532142331907378914627006853907252}\cdot t^5+\frac{1258960391394032296385931023512289518313691475763014050440817152138439442363151069026691754804543691231675509375}{150872010115159721954091995246443669655916966371876187532142331907378914627006853907252}\cdot t^3-\frac{69055039422845262347148530517663594466461692535445577437724367582425584715847724239266453953539164559945984375}{75436005057579860977045997623221834827958483185938093766071165953689457313503426953626}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.