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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{11}-\frac{6923}{82}\cdot t^9+\frac{97479}{164}\cdot t^7-\frac{566685}{328}\cdot t^5+\frac{1313235}{656}\cdot t^3-\frac{418635}{656}\cdot t$
• $P_4$:
  $4\cdot t^{43}-\frac{777206413554596144125804957212332944481327551817235951123089476858988125821291274138323393}{528052035403059026839321983362552843795709382301566656362498161675826201194523988675382}\cdot t^{41}+\frac{257748777342921895565304658506533665318135940070984369826513302588340377995361997490047998469}{1056104070806118053678643966725105687591418764603133312724996323351652402389047977350764}\cdot t^{39}-\frac{664150072640571300448298807123810410422859369507395128160284527686468028741294530795170206498275}{27458705840959069395644743134852747877376887879681466130849904407142962462115247411119864}\cdot t^{37}+\frac{87998855371762678816195569241718038156930711467045969969243162733491492400835456698552506786719325}{54917411681918138791289486269705495754753775759362932261699808814285924924230494822239728}\cdot t^{35}-\frac{590027830922071724814884872107452636428617032664301777700572447583504320963725630311050083389451465}{7845344525988305541612783752815070822107682251337561751671401259183703560604356403177104}\cdot t^{33}+\frac{20290643762847229349319169281399405989116853273609230666904945461700248842214159447195408048908962535}{7845344525988305541612783752815070822107682251337561751671401259183703560604356403177104}\cdot t^{31}-\frac{1043359537503517343845503257635176634318065054425189970341912348558553863043368603800772373393978427305}{15690689051976611083225567505630141644215364502675123503342802518367407121208712806354208}\cdot t^{29}+\frac{40578006669938432189917244135968531433121747500567849544445077233479109413660512289049271538749553283925}{31381378103953222166451135011260283288430729005350247006685605036734814242417425612708416}\cdot t^{27}-\frac{184641797831597437466388020908090253257706572584657649664846752597999714909573664480950956599178203901525}{9655808647370222205061887695772394857978685847800076002057109242072250536128438650064128}\cdot t^{25}+\frac{4155600522008653395520313844784294346578727943538186438557599852802519412205562396187659838122392412388125}{19311617294740444410123775391544789715957371695600152004114218484144501072256877300128256}\cdot t^{23}-\frac{70899266573925847782504632878863740947846331197932963744691108422061151924199442328170926654220664793993375}{38623234589480888820247550783089579431914743391200304008228436968289002144513754600256512}\cdot t^{21}+\frac{909480971954310413123483631284542115865865735601785674221598315570697697432833131280143269313707329628777625}{77246469178961777640495101566179158863829486782400608016456873936578004289027509200513024}\cdot t^{19}-\frac{1082171776745114105856960114141067497624189836931418626788351852227288142319621233376576891672140401756614375}{19311617294740444410123775391544789715957371695600152004114218484144501072256877300128256}\cdot t^{17}+\frac{29995764576108099168897808476050643836213770632650497066970305221570521980839185986365847194205383218951724375}{154492938357923555280990203132358317727658973564801216032913747873156008578055018401026048}\cdot t^{15}-\frac{147265464134235897899469802423174862504504386477191795965819467297248642697905036033281594623785349831437800625}{308985876715847110561980406264716635455317947129602432065827495746312017156110036802052096}\cdot t^{13}+\frac{3006971984395644718852183082299251292547647838098240889528272264967722200003910026065630629773948148880413125}{3768120447754233055633907393472154090918511550361005269095457265198927038489146790268928}\cdot t^{11}-\frac{4271160003602439426702072053830020150646039718239549876226393880619642772320285304844713293207224019298930814375}{4943774027453553768991686500235466167285087154073638913053239931940992274497760588832833536}\cdot t^9+\frac{5546006874667759120440300722089546048357060213623786323112067849405795840011417368378899033545017264011419196875}{9887548054907107537983373000470932334570174308147277826106479863881984548995521177665667072}\cdot t^7-\frac{3883562376215640774853717333279210845616952494215340612311734187169969548858850228140290179216872338380026440625}{19775096109814215075966746000941864669140348616294555652212959727763969097991042355331334144}\cdot t^5+\frac{1258960391394032296385931023512289518313691475763014050440817152138439442363151069026691754804543691231675509375}{39550192219628430151933492001883729338280697232589111304425919455527938195982084710662668288}\cdot t^3-\frac{69055039422845262347148530517663594466461692535445577437724367582425584715847724239266453953539164559945984375}{39550192219628430151933492001883729338280697232589111304425919455527938195982084710662668288}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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