Rule: Q[4, 15, 22]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{19}-\frac{93567}{667}\cdot t^{17}+\frac{56576166}{7337}\cdot t^{15}-\frac{1577757510}{7337}\cdot t^{13}+\frac{24226003620}{7337}\cdot t^{11}-\frac{18992429820}{667}\cdot t^9+\frac{3930143490}{29}\cdot t^7-\frac{224016557310}{667}\cdot t^5+\frac{250467132825}{667}\cdot t^3-\frac{83438061525}{667}\cdot t$
• $P_3$:
  $t^{41}-\frac{183040666278697947938063486844166976369695731455646257277091903864412094177731}{326915119611802177062684452066802854741902753040441489793534410477626357174}\cdot t^{39}+\frac{131753893497780254279153508481726236662381456850891290848393839224503603814785005979}{938573308405484050346967061883790995964002803979107517197237292481265271446554}\cdot t^{37}-\frac{112747479420179450388367143698688364382924069088148612921873732945339632985343457254}{5394099473594735921534293459102247103241395425167284581593317772880834893371}\cdot t^{35}+\frac{323383255009501980081327789326410666156083975435118099596820013559770247671105183571350}{156428884734247341724494510313965165994000467329851252866206215413544211907759}\cdot t^{33}-\frac{682226906166276488636253913006635816545639685552578247629919561295143931985114868397465}{4740269234371131567408924554968641393757589919086401602006248951925582179023}\cdot t^{31}+\frac{1503051193658546550001899698718711356117530015698239063021920679300253477913559741321715}{206098662363962242061257589346462669293808257351582678348097780518503573001}\cdot t^{29}-\frac{1300538826657401457510873101229717483504590133387998802388914720914895383434368840347653505}{4740269234371131567408924554968641393757589919086401602006248951925582179023}\cdot t^{27}+\frac{36725778838815430088543712696811316215379267146831925489809306156898828977611381718168711695}{4740269234371131567408924554968641393757589919086401602006248951925582179023}\cdot t^{25}-\frac{782028150279681163677940352124622955278285354135526457904192406883652821309425416460283510000}{4740269234371131567408924554968641393757589919086401602006248951925582179023}\cdot t^{23}+\frac{545521330299475230861223672082552929764555514379312655075928085493960968637858732701343209250}{206098662363962242061257589346462669293808257351582678348097780518503573001}\cdot t^{21}-\frac{6556881556600740928702442739267996011770890793189586987562678284722049345525126824766473614375}{206098662363962242061257589346462669293808257351582678348097780518503573001}\cdot t^{19}+\frac{58398058658121003568500432283802839076448087207902657835331864436011861032223289056343898309375}{206098662363962242061257589346462669293808257351582678348097780518503573001}\cdot t^{17}-\frac{378925477926550738125437459628792575665608415061382580312491795301784023884403020317074591130625}{206098662363962242061257589346462669293808257351582678348097780518503573001}\cdot t^{15}+\frac{1747838337748157610016370956544304929899039075575752672445216150173405648817336528407458688803125}{206098662363962242061257589346462669293808257351582678348097780518503573001}\cdot t^{13}-\frac{5533942295728277665493992681751419002342864186322740056288225082165856518107746774063969133533125}{206098662363962242061257589346462669293808257351582678348097780518503573001}\cdot t^{11}+\frac{11432379870220324654633407571172639519439371601926839113773566167398863182515954289705631759001250}{206098662363962242061257589346462669293808257351582678348097780518503573001}\cdot t^9-\frac{28543465795458005955802612900979454740140648881596524852892939456132389313371574105616583629069375}{412197324727924484122515178692925338587616514703165356696195561037007146002}\cdot t^7+\frac{18951588781225363003861505836017108751177662967203375203421956878430809593829633306057105914118125}{412197324727924484122515178692925338587616514703165356696195561037007146002}\cdot t^5-\frac{2575476936845141656464107290263634995322968591301152525002254573778780524950415447119987537796875}{206098662363962242061257589346462669293808257351582678348097780518503573001}\cdot t^3+\frac{113630886351313560313702913668001205548410336746780884618663576403986952880387544198909303221875}{206098662363962242061257589346462669293808257351582678348097780518503573001}\cdot t$

Warning: This rule has negative weights!

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.