Rule: Q[1, 2, 36, 78]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{4}\cdot t$
• $P_3$:
  $t^{39}-\frac{39}{4}\cdot t^{37}+\frac{351}{8}\cdot t^{35}-\frac{7735}{64}\cdot t^{33}+\frac{7293}{32}\cdot t^{31}-\frac{39897}{128}\cdot t^{29}+\frac{81809}{256}\cdot t^{27}-\frac{4102137}{16384}\cdot t^{25}+\frac{9924525}{65536}\cdot t^{23}-\frac{18599295}{262144}\cdot t^{21}+\frac{13468455}{524288}\cdot t^{19}-\frac{29910465}{4194304}\cdot t^{17}+\frac{6277505}{4194304}\cdot t^{15}-\frac{3900225}{16777216}\cdot t^{13}+\frac{869193}{33554432}\cdot t^{11}-\frac{1062347}{536870912}\cdot t^9+\frac{415701}{4294967296}\cdot t^7-\frac{46683}{17179869184}\cdot t^5+\frac{1235}{34359738368}\cdot t^3-\frac{39}{274877906944}\cdot t$
• $P_4$:
  $t^{117}-\frac{117}{4}\cdot t^{115}+\frac{6669}{16}\cdot t^{113}-\frac{30849}{8}\cdot t^{111}+\frac{1666665}{64}\cdot t^{109}-\frac{140142717}{1024}\cdot t^{107}+\frac{2386634679}{4096}\cdot t^{105}-\frac{8461704771}{4096}\cdot t^{103}+\frac{407792065707}{65536}\cdot t^{101}-\frac{4237345538725}{262144}\cdot t^{99}+\frac{38421239641785}{1048576}\cdot t^{97}-\frac{19177668500445}{262144}\cdot t^{95}+\frac{271835840807895}{2097152}\cdot t^{93}-\frac{3440573156734245}{16777216}\cdot t^{91}+\frac{19541119385335275}{67108864}\cdot t^{89}-\frac{25007524023847365}{67108864}\cdot t^{87}+\frac{926268785873395965}{2147483648}\cdot t^{85}-\frac{3890328900668263053}{8589934592}\cdot t^{83}+\frac{14858349325447922749}{34359738368}\cdot t^{81}-\frac{6463621349953177995}{17179869184}\cdot t^{79}+\frac{41060654390114930727}{137438953472}\cdot t^{77}-\frac{953519640837113391327}{4398046511104}\cdot t^{75}+\frac{2532073687390420728165}{17592186044416}\cdot t^{73}-\frac{1538919900661893079005}{17592186044416}\cdot t^{71}+\frac{13706867215572775273575}{281474976710656}\cdot t^{69}-\frac{27962009119768461558093}{1125899906842624}\cdot t^{67}+\frac{52260356858671232886681}{4503599627370496}\cdot t^{65}-\frac{2795821560340436327271}{562949953421312}\cdot t^{63}+\frac{8764429385786311632681}{4503599627370496}\cdot t^{61}-\frac{25139350746064185404085}{36028797018963968}\cdot t^{59}+\frac{32960482089284154196467}{144115188075855872}\cdot t^{57}-\frac{9865890737902758833001}{144115188075855872}\cdot t^{55}+\frac{172362914656301139611841}{9223372036854775808}\cdot t^{53}-\frac{171368034918025231158093}{36893488147419103232}\cdot t^{51}+\frac{154850633962070992010325}{147573952589676412928}\cdot t^{49}-\frac{15862747869285321132765}{73786976294838206464}\cdot t^{47}+\frac{23522126813028027633085}{590295810358705651712}\cdot t^{45}-\frac{62937582553777695558795}{9444732965739290427392}\cdot t^{43}+\frac{37863182575657068014385}{37778931862957161709568}\cdot t^{41}-\frac{5103190287974818502925}{37778931862957161709568}\cdot t^{39}+\frac{9821984424387897430305}{604462909807314587353088}\cdot t^{37}-\frac{4198614651246687861735}{2417851639229258349412352}\cdot t^{35}+\frac{1586143312693193192211}{9671406556917033397649408}\cdot t^{33}-\frac{32899264185339645093}{2417851639229258349412352}\cdot t^{31}+\frac{19051255101099545415}{19342813113834066795298816}\cdot t^{29}-\frac{9549147618575821529}{154742504910672534362390528}\cdot t^{27}+\frac{2052511215015378663}{618970019642690137449562112}\cdot t^{25}-\frac{93579538678512705}{618970019642690137449562112}\cdot t^{23}+\frac{114374991718182195}{19807040628566084398385987584}\cdot t^{21}-\frac{14417015762796075}{79228162514264337593543950336}\cdot t^{19}+\frac{1471826683843659}{316912650057057350374175801344}\cdot t^{17}-\frac{14866936200441}{158456325028528675187087900672}\cdot t^{15}+\frac{1847370770469}{1267650600228229401496703205376}\cdot t^{13}-\frac{1359386038647}{81129638414606681695789005144064}\cdot t^{11}+\frac{43954281085}{324518553658426726783156020576256}\cdot t^9-\frac{232016733}{324518553658426726783156020576256}\cdot t^7+\frac{11410659}{5192296858534827628530496329220096}\cdot t^5-\frac{66729}{20769187434139310514121985316880384}\cdot t^3+\frac{117}{83076749736557242056487941267521536}\cdot t$

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.