Rule: Q[38, 76]

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.

• $P_1$:
  $137438953472\cdot t^{38}-1305670057984\cdot t^{36}+5712306503680\cdot t^{34}-15260018802688\cdot t^{32}+27827093110784\cdot t^{30}-36681168191488\cdot t^{28}+36108024938496\cdot t^{26}-27039419596800\cdot t^{24}+15547666268160\cdot t^{22}-6880289095680\cdot t^{20}+2334383800320\cdot t^{18}-601280675840\cdot t^{16}+115630899200\cdot t^{14}-16188325888\cdot t^{12}+1589924864\cdot t^{10}-103690752\cdot t^8+4124064\cdot t^6-86640\cdot t^4+722\cdot t^2-1$
• $P_2$:
  $137438953472\cdot t^{114}-3917010173952\cdot t^{112}+54348516163584\cdot t^{110}-489218249850880\cdot t^{108}+3212162554134528\cdot t^{106}-16399710654824448\cdot t^{104}+67775347428425728\cdot t^{102}-233051278106689536\cdot t^{100}+680190935511859200\cdot t^{98}-1710554241527971840\cdot t^{96}+3750061221811322880\cdot t^{94}-7233679435365089280\cdot t^{92}+12369355439721512960\cdot t^{90}-18864915664921804800\cdot t^{88}+25791034701900238848\cdot t^{86}-31739471998466455552\cdot t^{84}+35281823784009586752\cdot t^{82}-35527876527197039904\cdot t^{80}+32484979695006552690\cdot t^{78}-27022823829391877487\cdot t^{76}+\frac{163861804071844363485}{8}\cdot t^{74}-\frac{226620958933974206745}{16}\cdot t^{72}+\frac{572374674936006000435}{64}\cdot t^{70}-\frac{660432317233853077425}{128}\cdot t^{68}+\frac{5572091920958212260645}{2048}\cdot t^{66}-\frac{5371747042901287774869}{4096}\cdot t^{64}+\frac{2366573872047420488229}{4096}\cdot t^{62}-\frac{1905147378476659064811}{8192}\cdot t^{60}+\frac{5601513056318416187235}{65536}\cdot t^{58}-\frac{3756308755413526149087}{131072}\cdot t^{56}+\frac{4591044034394309737773}{524288}\cdot t^{54}-\frac{2553355621149730755831}{1048576}\cdot t^{52}+\frac{41289628702982231490633}{67108864}\cdot t^{50}-\frac{18922482289993727488225}{134217728}\cdot t^{48}+\frac{31389058857519006774585}{1073741824}\cdot t^{46}-\frac{11749611543411273783615}{2147483648}\cdot t^{44}+\frac{15833522108357642449145}{17179869184}\cdot t^{42}-\frac{4785069334958206440405}{34359738368}\cdot t^{40}+\frac{2584732743259973007975}{137438953472}\cdot t^{38}-\frac{621219527696328555421}{274877906944}\cdot t^{36}+\frac{1057752168780235107879}{4398046511104}\cdot t^{34}-\frac{198262267519449346983}{8796093022208}\cdot t^{32}+\frac{32519207900015501357}{17592186044416}\cdot t^{30}-\frac{4633427918934406515}{35184372088832}\cdot t^{28}+\frac{2274591887476890471}{281474976710656}\cdot t^{26}-\frac{238081276466985315}{562949953421312}\cdot t^{24}+\frac{42014342905938585}{2251799813685248}\cdot t^{22}-\frac{3082030235399115}{4503599627370496}\cdot t^{20}+\frac{2957503761241575}{144115188075855872}\cdot t^{18}-\frac{142071609252735}{288230376151711744}\cdot t^{16}+\frac{85242965551641}{9223372036854775808}\cdot t^{14}-\frac{2414288784687}{18446744073709551616}\cdot t^{12}+\frac{197696103957}{147573952589676412928}\cdot t^{10}-\frac{2751724305}{295147905179352825856}\cdot t^8+\frac{47560667}{1180591620717411303424}\cdot t^6-\frac{219849}{2361183241434822606848}\cdot t^4+\frac{3249}{37778931862957161709568}\cdot t^2-\frac{1}{75557863725914323419136}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.