Rule: Q[2, 63]

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^{65}-\frac{1108195160285199591026688614062076721785278}{274662905080377442409531016691131991427}\cdot t^{63}+\frac{524279254251641169810714793009925908396115727}{274662905080377442409531016691131991427}\cdot t^{61}-\frac{5074822214940336393026488702040428573805694705}{9005341150176309587197738252168262014}\cdot t^{59}+\frac{2098905894820062680368828557495628571726386797885}{18010682300352619174395476504336524028}\cdot t^{57}-\frac{647036462634047352783688042003753651665558149277435}{36021364600705238348790953008673048056}\cdot t^{55}+\frac{14042298681934440704857035190235309922811206735074505}{6549339018310043336143809637940554192}\cdot t^{53}-\frac{204826479598271213291513640021561892059088520258444655}{1007590618201545128637509175067777568}\cdot t^{51}+\frac{31398857035101812428430181579010314949764205292284245375}{2015181236403090257275018350135555136}\cdot t^{49}-\frac{3940056534205942297833982565865669238074527215334839517625}{4030362472806180514550036700271110272}\cdot t^{47}+\frac{408329273817375950785968820591198389918630066588191185505625}{8060724945612361029100073400542220544}\cdot t^{45}-\frac{35166459265838058525847571323108614168126336707881759724038875}{16121449891224722058200146801084441088}\cdot t^{43}+\frac{2527142112580449181442085646673955336579091548567680034631005375}{32242899782449444116400293602168882176}\cdot t^{41}-\frac{151889745817953788940584313234836131903498041007011636386386925625}{64485799564898888232800587204337764352}\cdot t^{39}+\frac{7641570068585522890667347792034748217805525556595562878998016610625}{128971599129797776465601174408675528704}\cdot t^{37}-\frac{321626179711179658572631902564728307878427315972322723528832131606875}{257943198259595552931202348817351057408}\cdot t^{35}+\frac{11303759736525715623486373130128294247333883240807653803871289612043125}{515886396519191105862404697634702114816}\cdot t^{33}-\frac{330684720184831947195763683444531670587744726657430925905850760365679375}{1031772793038382211724809395269404229632}\cdot t^{31}+\frac{8015772338596076422505390537088061792113820637813358747205952600760009375}{2063545586076764423449618790538808459264}\cdot t^{29}-\frac{160025029757970262222954860504637359834138232446268032009931690535882128125}{4127091172153528846899237581077616918528}\cdot t^{27}+\frac{2610837352704828660168996698769952030844114790937085550839835281693920865625}{8254182344307057693798475162155233837056}\cdot t^{25}-\frac{34474791902246845976073365652621691379987194320602387712933848492615862609375}{16508364688614115387596950324310467674112}\cdot t^{23}+\frac{363996934378741320421923666640949639529600896577048005473791290480449269234375}{33016729377228230775193900648620935348224}\cdot t^{21}-\frac{3027047391093270501956120084265976692163621838178495477054656430092234125078125}{66033458754456461550387801297241870696448}\cdot t^{19}+\frac{19455842146375117666731090061158824465672248519982339757152322894841631104453125}{132066917508912923100775602594483741392896}\cdot t^{17}-\frac{94351205673786115558215045399258753598252081449609371867178789865501951728421875}{264133835017825846201551205188967482785792}\cdot t^{15}+\frac{334637544518677579076475418881169912340036490377079062416236116700841160619421875}{528267670035651692403102410377934965571584}\cdot t^{13}-\frac{832697302135965775373793557210962923762825438599903022176722792507337268969515625}{1056535340071303384806204820755869931143168}\cdot t^{11}+\frac{1372375557352766585478951478725318729678353186407464018649753641666908875373203125}{2113070680142606769612409641511739862286336}\cdot t^9-\frac{1376808454918676356016570120483418682242814846514334332128069227137882389399921875}{4226141360285213539224819283023479724572672}\cdot t^7+\frac{734984800841673865524247228543060914178061464517720021187097201785928322421796875}{8452282720570427078449638566046959449145344}\cdot t^5-\frac{163291510722669123173192055725073790576178237572711616091789014379141603956015625}{16904565441140854156899277132093918898290688}\cdot t^3+\frac{4194897665910403701858016889401158075517796498484254010816451925878270495546875}{16904565441140854156899277132093918898290688}\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.