Rule: Q[12, 26]

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.

• $P_1$:
  $\frac{676039}{1024}\cdot t^{12}-\frac{969969}{512}\cdot t^{10}+\frac{2078505}{1024}\cdot t^8-\frac{255255}{256}\cdot t^6+\frac{225225}{1024}\cdot t^4-\frac{9009}{512}\cdot t^2+\frac{231}{1024}$
• $P_2$:
  $\frac{676039}{1024}\cdot t^{38}-\frac{642844607231824366161323061033355382950511}{101315073343332573176365079746587952128}\cdot t^{36}+\frac{829543499171682542422999573255454974787389095}{29527715264395704382400622686144466492416}\cdot t^{34}-\frac{132375106477459247314193426346905161859152797045}{1742135200599346558561636738482523523052544}\cdot t^{32}+\frac{2506092667036791767635730196007825607106660165275}{17856885806143302225256776569445866111288576}\cdot t^{30}-\frac{3347499095153580224353214782459392575764871255427}{17856885806143302225256776569445866111288576}\cdot t^{28}+\frac{23548474731146766441269128093716244440069897274804041}{125873188047504137385835018038023910218473172224}\cdot t^{26}-\frac{415969931701224874223699011007224452358401432248675}{2927283442965212497345000419488928144615655168}\cdot t^{24}+\frac{17389291516123966673007854833229633351343990516330094725}{209704731287141892884801140051347834423976304925184}\cdot t^{22}-\frac{27227092741053772756058215500874960357995772599007875}{730678506226975236532408153489016844682844268032}\cdot t^{20}+\frac{60764170294673525271464825870893672839898889021682365}{4730181908732523899657168572586793257683676050944}\cdot t^{18}-\frac{630619860092567336790463154910963156753519544151373555}{187445051716635898062885052650939395564288417626624}\cdot t^{16}+\frac{2529586466253917630469685194127490168634534384253806975}{3842623560191035910289143579344257609067912561345792}\cdot t^{14}-\frac{360617497502659928184530801174995579799591217513528775}{3842623560191035910289143579344257609067912561345792}\cdot t^{12}+\frac{36095845110401662979916550617424360818793280723497125}{3842623560191035910289143579344257609067912561345792}\cdot t^{10}-\frac{16809446342686463402500695053532588269272019093919435}{26898364921337251372024005055409803263475387929420544}\cdot t^8+\frac{390095884194581155589339164225046134248089919760315}{15370494240764143641156574317377030436271650245383168}\cdot t^6-\frac{8377476470137862746779699084238955264768045967075}{15370494240764143641156574317377030436271650245383168}\cdot t^4+\frac{71450880390670348833669783285873252985929440925}{15370494240764143641156574317377030436271650245383168}\cdot t^2-\frac{101421289318555856047400565502806253584223125}{15370494240764143641156574317377030436271650245383168}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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