Rule: Q[4, 47]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{51}-\frac{8183125494081144304867576559086425}{149543807463080600475948040277192}\cdot t^{49}+\frac{63873244469804037196025700930821556594}{198538097383172382206880516973007029}\cdot t^{47}-\frac{5244077418429883124339881691149951559}{4437405204670759804191273270485377}\cdot t^{45}+\frac{973255163832957335752536297507948789683595}{320043412981673880117491393360487330748}\cdot t^{43}-\frac{3858675518214375522124927863386830155191415}{662415436171371519312947302536822614804}\cdot t^{41}+\frac{41381431037014059658032358574879054374876875}{4802511912242443515018867943391963957329}\cdot t^{39}-\frac{195934041556609115268865680452356386195576}{19443368065758880627606752807254914807}\cdot t^{37}+\frac{122171784410114829812583169432114392826103133}{12910396395663896736730883864017263431848}\cdot t^{35}-\frac{837387486927118272709004941856379584721424495}{116193567560975070630577954776155370886632}\cdot t^{33}+\frac{570834876368390859888581985929172381526553560}{127490164407180980275217478157170476389499}\cdot t^{31}-\frac{28071655987179111568764177404474152859799950}{12337757845856223897601691434564884811887}\cdot t^{29}+\frac{12066752959936231080258054967267811133043499}{12763197771575404032001749759894708426090}\cdot t^{27}-\frac{2550662611571296176829182947084191528463457}{7963362712179525592616476345917211240210}\cdot t^{25}+\frac{4973964328665696819277827790736865398308230}{56539875256474631707576982056012199805491}\cdot t^{23}-\frac{14274106948222955667057973967916193067662860}{735018378334170212198500766728158597471383}\cdot t^{21}+\frac{15068866999655565005157550432934780847849825}{4426627536933879030768498999621269755557992}\cdot t^{19}-\frac{2387340853387332798258065089303186807198731591}{5121608060232498038599153342561809107180596744}\cdot t^{17}+\frac{1185883378647370578778074075746732256347758}{24311430665660591955375727891907321711300301}\cdot t^{15}-\frac{147908295371837118528020353816525900071736035}{39052261459272797544318544237033794442252050173}\cdot t^{13}+\frac{148529782333241210911250831448893356078180655}{708948746491413863112244341533844268336267987756}\cdot t^{11}-\frac{314841398985510308836013843652960914025382825}{40410078550010590197397927467429123295167275302092}\cdot t^9+\frac{31625809641729941460025031460634084604697}{177237186622853465778061085383461067084066996939}\cdot t^7-\frac{388367358516555757916141773456571330255388}{178477846929213440038507512981145294553655465917573}\cdot t^5+\frac{15157210298384905489752427787258985642795}{1427822775433707520308060103849162356429243727340584}\cdot t^3-\frac{12685541843957367794894258220149897265}{1427822775433707520308060103849162356429243727340584}\cdot t$

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.