Rule: Q[16, 34]

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.

• $P_1$:
  $\frac{300540195}{32768}\cdot t^{16}-\frac{145422675}{4096}\cdot t^{14}+\frac{456326325}{8192}\cdot t^{12}-\frac{185910725}{4096}\cdot t^{10}+\frac{334639305}{16384}\cdot t^8-\frac{20369349}{4096}\cdot t^6+\frac{4849845}{8192}\cdot t^4-\frac{109395}{4096}\cdot t^2+\frac{6435}{32768}$
• $P_2$:
  $\frac{300540195}{32768}\cdot t^{50}-\frac{29355809106181565752688432681879616954595562668616820768550261935834799130678289}{253737493588473484148652561120003695894068143768692752357165411670248161280}\cdot t^{48}+\frac{8703844190128762895094306493685348587686041403695692207915467054783052867813833}{12686874679423674207432628056000184794703407188434637617858270583512408064}\cdot t^{46}-\frac{32250609151769655588122985648494328487752413427707840646919795223989826227567759}{12686874679423674207432628056000184794703407188434637617858270583512408064}\cdot t^{44}+\frac{1600515595847693282099637459845928693475682962921768044024136714885931240381678640597}{242547670121221803497696983174611532905139738628493401978214417015590217367552}\cdot t^{42}-\frac{46396283375964985182724171204256136075369604538939856145624186821799220362570158771977}{3638215051818327052465454747619172993577096079427401029673216255233853260513280}\cdot t^{40}+\frac{223260943327328887372877074556594873697652690397355771783101994000051500266782052513851323}{11730211696237589471657370348782150260124820609420512153171394742916481887438233600}\cdot t^{38}-\frac{3741334418245545569893278601003777551755202943206783017930645226522098795210603946136085111}{166569006086573770497534658952706533693772452653771272575033805349414042801622917120}\cdot t^{36}+\frac{127640252243619922681973534895006123300464477438556415902591491969922293838684134250061453361}{5996484219116655737911247722297435212975808295535765812701216992578905540858425016320}\cdot t^{34}-\frac{2972995672605948105836089562109579134049287920135010956617021511332103980066014591101895827}{181711643003535022360946900675679854938660857440477751900036878562997137601770455040}\cdot t^{32}+\frac{5360076782795447280301094312891315301894998026161452336002556442399724082720756677497320911}{522420973635163189287722339442579582948649965141373536712606025868616770605090058240}\cdot t^{30}-\frac{11248122779272306242932502192359923740603062844196941305683690845828656493869541559552061887}{2137176710325667592540682297719643748426295311941982650187933742189795879748095692800}\cdot t^{28}+\frac{768954544871828621362770926379654107653748323379575477327975365699994512662411338016050177}{348280649090108792858481559628386388632433310094249024475070683912411180403393372160}\cdot t^{26}-\frac{3103711097389604936129336886558334570317511871781173797530298271675896245114364390209650053}{4109711659263283755730082403614959385862713059112138488805834070166451928760041791488}\cdot t^{24}+\frac{65062590550981894697238928976876854417179563342713963774774991089995488746343075596656844981}{310640596505618209101597750377591604014014202315932728816910544825407681658666637152256}\cdot t^{22}-\frac{53180687878303616940984953811252693798909830142073999678305416389829513847440296721736992755}{1139015520520600100039191751384502548051385408491753338995338664359828166081777669558272}\cdot t^{20}+\frac{210089131712543240307134856966225922060466772839701090437390991087915267951509552648342449887}{25418030563196549600874594873001530545988811221079127143895978615187744337824933257510912}\cdot t^{18}-\frac{5839913024265587010235570991145614257141196911664290494776147637935077828607151376021142086645}{5109024143202506469775793569473307639743751055436904555923091701652736611902811584759693312}\cdot t^{16}+\frac{51436323395659822682154436873198790221284695734493521135518510050640738302147910281192102065}{425752011933542205814649464122775636645312587953075379660257641804394717658567632063307776}\cdot t^{14}-\frac{4033698857603740884941605818935312024955478669601961411065555192613539646281920980872106055}{425752011933542205814649464122775636645312587953075379660257641804394717658567632063307776}\cdot t^{12}+\frac{368739629509486473536534590646738477770887861376150734042586355456286103838043690962054141}{696685110436705427696699123109996496328693325741396075807694322952645901623110670649049088}\cdot t^{10}-\frac{7691999700215667849432751505854529863043945860997294217209449565612541654302374832606051}{387047283575947459831499512838886942404829625411886708782052401640358834235061483693916160}\cdot t^8+\frac{1616187724461014082993259604793685720664022533188463516900841779602066567144502600497}{3518611668872249634831813753080790385498451140108060988927749105821443947591468033581056}\cdot t^6-\frac{655488143389769708360017912655733218761898514639503944710731907244228279768658855039}{116114185072784237949449853851666082721448887623566012634615720492107650270518445108174848}\cdot t^4+\frac{4279015947797062898455908386107511920608771186143543184192285799316340085335631057}{154818913430378983932599805135554776961931850164754683512820960656143533694024593477566464}\cdot t^2-\frac{3488809078671113483602462826934162888783316827890242816277384011384551356627635}{154818913430378983932599805135554776961931850164754683512820960656143533694024593477566464}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.