Rule: Q[1, 32, 34]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{33}-\frac{528}{65}\cdot t^{31}+\frac{2728}{91}\cdot t^{29}-\frac{158224}{2379}\cdot t^{27}+\frac{356004}{3599}\cdot t^{25}-\frac{7120080}{68381}\cdot t^{23}+\frac{5458728}{68381}\cdot t^{21}-\frac{163761840}{3624193}\cdot t^{19}+\frac{61410690}{3242699}\cdot t^{17}-\frac{54587280}{9346603}\cdot t^{15}+\frac{81880920}{62755763}\cdot t^{13}-\frac{12902448}{62755763}\cdot t^{11}+\frac{59136220}{2698497809}\cdot t^9-\frac{163761840}{110638410169}\cdot t^7+\frac{81880920}{1438299332197}\cdot t^5-\frac{54587280}{53217075291289}\cdot t^3+\frac{2047023}{372519527039023}\cdot t$
• $P_3$:
  $t^{67}-\frac{75107}{4485}\cdot t^{65}+\frac{316931708}{2366217}\cdot t^{63}-\frac{70736510373716}{103862390967}\cdot t^{61}+\frac{1216737755363236748}{492139169631027}\cdot t^{59}-\frac{4102719886265249598436}{601452454682122065}\cdot t^{57}+\frac{66492194609850925322830602196}{4471725085220436355642275}\cdot t^{55}-\frac{85955960845619029676529141390196}{3270619727330227150516759935}\cdot t^{53}+\frac{16361195055823924875859871304870972376}{426568356384022538593366931440155}\cdot t^{51}-\frac{290032750432150208492903843119635140595776}{6193095043777044401049686614678763295}\cdot t^{49}+\frac{2241933086673416741796340909445642138777779818316}{46417062192206108329335818773121606316673425}\cdot t^{47}-\frac{1284849065567234077827111982318788087661116269768516}{30324167970461458643665027987844657913903351375}\cdot t^{45}+\frac{234084394269332274330946253699882419362554185549092127057748}{7367917184033846315801220419883541250641884104381932725}\cdot t^{43}-\frac{306988805291439370190256796376132103034855103643738657982242868}{15026952770292657861615144874496899631163781257446305070925}\cdot t^{41}+\frac{1816789777578411409123960331968262805557301460507024290529528612}{160979233150820605758231073443580159261552184515219988402355}\cdot t^{39}-\frac{9568289255767762123476109433985838195849137536256047686011757129129671196}{1785264638633784593152267492326899492449850128588655353146645450773625}\cdot t^{37}+\frac{1501562756292629777544448123031206734453905816663349240966047915103754664842958}{686680089320469612080617413039514626547346617318153096772027936864936964375}\cdot t^{35}-\frac{104620603809716511970783001771847364735017698408850808914806905662123669551116046}{136727815499267220759709221470639355211670245031148826611550362628907020135125}\cdot t^{33}+\frac{12996279365379332947657785570642181870823407644901756430878336131270206526148}{56757084059471656604279460967471712416633559581215785226878523299670826125}\cdot t^{31}-\frac{101403969111125973679952286243378916926234824687066641486048992689764920297436}{1737499121691567810240684143810666293012427356212057425171216729399600451375}\cdot t^{29}+\frac{1358942021647535004512582843134317374647374584381176609063665726278795760244}{107844773070511105463214877891696528531805835902817357424420348721354510775}\cdot t^{27}-\frac{214485003125242323639961488985877425091992381406593657241886505582721393068}{93711270047025319562052814122414362399432421510995139642302582222259617625}\cdot t^{25}+\frac{76677560675495430380314137995994802864440689015480648357531794901080169948}{221158597310979754166444641328897895262660514765948529555834094044532697595}\cdot t^{23}-\frac{166236602144284285406425475609412799786197080518758817367351622332952266668}{3836620883786127039670061386531750443904415017026672317077295805381241145235}\cdot t^{21}+\frac{211902782224263466257139402744694767618688094529727250038006687458664416}{48077955937169511775314052462803890274491416253467071642572629140115803825}\cdot t^{19}-\frac{15543240361498185105883206730781083516847276803425543926283078711923684888}{43318238299389730109557961268986305137316766044373831549957938855244339246325}\cdot t^{17}+\frac{9621252068634028857271243033292312223261675537531252740153626158960892772}{420441724670547380475121388787220020450427435136569541514297641830312704449625}\cdot t^{15}-\frac{2836746792230461546116828973110244483406208715788005567205917791475163076}{2550679796334654108215736425309134790732593106495188551853405693770563740327725}\cdot t^{13}+\frac{366201681901305194642781664288214429793902307483839647876426109118977588}{9221688494440672545087662460733025781879375077328758610546928277478191984261775}\cdot t^{11}-\frac{7475228890327402447125636128436526226167807596915366601215793220644028}{7545017859087822991435360195145202912446761426905347954083850408845793441668725}\cdot t^9+\frac{4053227927900001465900869528960077799137238674826834795363371568963812}{252338930620603857824671490970967341849608354388723303797693219229175980660254025}\cdot t^7-\frac{1116565155317529726388537551746465764510802187630109996695387155334268}{7389925825317684407722522235578329297024244664241182468361015705997296576478867875}\cdot t^5+\frac{948080646070657489792821534824587092660878013721175550072862321021}{1405888327743364350737455449695389476019246545880029835444290792848266177964272425}\cdot t^3-\frac{640754947652224554503662437292524187649994070518891591848921219533}{710910864395561240022906639062635278373732336700001753456329710916939930657267089575}\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.