Rule: Q[12, 37]

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^{49}-\frac{11861487707756676301329398743689009270130349558154828078780469967830479}{1499758685835304192919911116029448956784757994635710812328171001600}\cdot t^{47}+\frac{160474790481950740988592037845792558596095966989484053313718141650247619051}{3609919156805577192358226056282883638980912493088155925273907600851200}\cdot t^{45}-\frac{17885019782484572074916069688213193418648642828783109889621498590281312747161}{114795429186417354716991588589795699719593017280203358423710261707068160}\cdot t^{43}+\frac{3697518744650198318034186486341893716212283114441643531994063764757229395340379}{9687996582021583502099844347895449132158745643077081822955210600451125760}\cdot t^{41}-\frac{10440114452794927597922664625113585428312675187819073432454136129524533784280498975}{15036739494955699753609168412368526598023589112619938697408782372960192292096}\cdot t^{39}+\frac{3368138633886957856256134605797562577684612221637304142367673173219405399773409997891}{3462407120549009811686321673900647571913326440405906936903338046405307435680000}\cdot t^{37}-\frac{38794526358897459130312145261038190467154389747349203199714058896977360223489607425583}{36107959971439673750443068884963896107096118592804458056277668198226777543520000}\cdot t^{35}+\frac{10416084112968752770458133940321673065352745631186788234883568781849713953600573889167}{10967551477956007855749552474149461491353259551183386190355997613151235104128000}\cdot t^{33}-\frac{8369801300583067075255570072284880241630764666651283107358905255702895853839590303939}{12338495412700508837718246533418144177772416995081309464150497314795139492144000}\cdot t^{31}+\frac{21694110902843953413473415278673303045110327615064884918298768590294548560703567044721}{55111946176728939475141501182601043994050129244696515606538888006084956398243200}\cdot t^{29}-\frac{38284408858487904206223085257573520612842195798544341204618358342152398638559140471303}{205877959855596612981850435452245279288118298902601926116380903471007021027920000}\cdot t^{27}+\frac{323290205159967184277148006120064577569533305133653166809357554128797842802112114647}{4524790326496628856743965614335061083255347228628613760799580296066088374240000}\cdot t^{25}-\frac{98632345232087786853857480513469586308770411318644470404624275313224163019596946009}{4434294519966696279609086302048359861590240284056041485583588690144766606755200}\cdot t^{23}+\frac{3530274067595792776781666803525265860060563198196561313855081119178978998676555163}{633470645709528039944155186006908551655748612008005926511941241449252372393600}\cdot t^{21}-\frac{2677952361989870165006089621061723737893660267605169771674253664351148245098987763}{2407188453696206551787789706826252496291844725630422520745376717507159015095680}\cdot t^{19}+\frac{48634687833575099150308078984462649830152254525891607230519283149137514748278134563}{278727084112192337575428281843039762728529389283522607665254146237671043853184000}\cdot t^{17}-\frac{4597854597981739293158941659032340933374051265046467081788827562607307904015546567673}{217894898004706359899591059330796334513027850072393798542312428821299338532226592000}\cdot t^{15}+\frac{15297077844324961053865084442715239464779371879038100710510504143180195248968195787297}{7974953266972252772325032771507145843176819312649613026648634894859555790279493267200}\cdot t^{13}-\frac{214173596594777447306963548535532315270056124846954680979005333248678049874595278647}{1691656753600174830493188769713636997037507126925675490501225583758087591877468268800}\cdot t^{11}+\frac{27383217407918852046757648923963556969008255235008445302377009330833354631112914841}{4736638910080489525380928555198183591705019955391891373403431634522645257256911152640}\cdot t^9-\frac{27154935910958350767699518167713305898099296194909539318260082780150014221299759}{159590259773601399103131016010720471418632747823176933066153356958310150177119648000}\cdot t^7+\frac{415325050137329968923164011430355184603828502621541965935514659648605023067915603}{143790824056014860591921045425659144748188105788682416692604174619437445309584802848000}\cdot t^5-\frac{12676790411979285315181030437759794037674285018450665272891668215409692344367887}{546405131412856470249299972617504750043114801996993183431895863553862292176422250822400}\cdot t^3+\frac{1590093335502797523550518658884767676554105687132358329075495578135962864228961}{28413066833468536452963598576110247002241969703843645538458584904800839193173957042764800}\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.