Rule: Q[1, 30, 32, 62]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{31}-\frac{31}{4}\cdot t^{29}+\frac{217}{8}\cdot t^{27}-\frac{3627}{64}\cdot t^{25}+\frac{10075}{128}\cdot t^{23}-\frac{39215}{512}\cdot t^{21}+\frac{54901}{1024}\cdot t^{19}-\frac{447051}{16384}\cdot t^{17}+\frac{330429}{32768}\cdot t^{15}-\frac{350455}{131072}\cdot t^{13}+\frac{130169}{262144}\cdot t^{11}-\frac{130169}{2097152}\cdot t^9+\frac{20553}{4194304}\cdot t^7-\frac{3689}{16777216}\cdot t^5+\frac{155}{33554432}\cdot t^3-\frac{31}{1073741824}\cdot t$
• $P_3$:
  $t^{63}-16\cdot t^{61}+\frac{1951}{16}\cdot t^{59}-\frac{9425}{16}\cdot t^{57}+\frac{259217}{128}\cdot t^{55}-\frac{337491}{64}\cdot t^{53}+\frac{44268939}{4096}\cdot t^{51}-\frac{73264815}{4096}\cdot t^{49}+\frac{797362475}{32768}\cdot t^{47}-\frac{225761445}{8192}\cdot t^{45}+\frac{13747006735}{524288}\cdot t^{43}-\frac{11058073285}{524288}\cdot t^{41}+\frac{60419672509}{4194304}\cdot t^{39}-\frac{17561974645}{2097152}\cdot t^{37}+\frac{1113356771979}{268435456}\cdot t^{35}-\frac{469578464931}{268435456}\cdot t^{33}+\frac{1346790732573}{2147483648}\cdot t^{31}-\frac{51138429529}{268435456}\cdot t^{29}+\frac{1676887120055}{34359738368}\cdot t^{27}-\frac{360026437953}{34359738368}\cdot t^{25}+\frac{514057545105}{274877906944}\cdot t^{23}-\frac{37743692415}{137438953472}\cdot t^{21}+\frac{288075375705}{8796093022208}\cdot t^{19}-\frac{27444469725}{8796093022208}\cdot t^{17}+\frac{16361903385}{70368744177664}\cdot t^{15}-\frac{232041789}{17592186044416}\cdot t^{13}+\frac{618457161}{1125899906842624}\cdot t^{11}-\frac{17988091}{1125899906842624}\cdot t^9+\frac{2719475}{9007199254740992}\cdot t^7-\frac{14911}{4503599627370496}\cdot t^5+\frac{19871}{1152921504606846976}\cdot t^3-\frac{31}{1152921504606846976}\cdot t$
• $P_4$:
  $t^{125}-\frac{63}{2}\cdot t^{123}+\frac{1937}{4}\cdot t^{121}-\frac{38735}{8}\cdot t^{119}+\frac{9064111}{256}\cdot t^{117}-\frac{103363221}{512}\cdot t^{115}+\frac{59803887}{64}\cdot t^{113}-\frac{3696118469}{1024}\cdot t^{111}+\frac{388998086785}{32768}\cdot t^{109}-\frac{2211929464503}{65536}\cdot t^{107}+\frac{11001957499863}{131072}\cdot t^{105}-\frac{48320938759821}{262144}\cdot t^{103}+\frac{6042787916861163}{16777216}\cdot t^{101}-\frac{21144930918399825}{33554432}\cdot t^{99}+\frac{33298961780530845}{33554432}\cdot t^{97}-\frac{47406704798010285}{33554432}\cdot t^{95}+\frac{3919325399610664715}{2147483648}\cdot t^{93}-\frac{9216440965453422085}{4294967296}\cdot t^{91}+\frac{19778011110752414975}{8589934592}\cdot t^{89}-\frac{38817380755402514265}{17179869184}\cdot t^{87}+\frac{1116900291004325273215}{549755813888}\cdot t^{85}-\frac{1843189187705589251605}{1099511627776}\cdot t^{83}+\frac{698703349858613857205}{549755813888}\cdot t^{81}-\frac{1948778234100431686575}{2199023255552}\cdot t^{79}+\frac{40022724663775730454669}{70368744177664}\cdot t^{77}-\frac{47309630267414248985979}{140737488355328}\cdot t^{75}+\frac{51517750891099752286983}{281474976710656}\cdot t^{73}-\frac{51688095087447038364117}{562949953421312}\cdot t^{71}+\frac{3057816305066456056323915}{72057594037927936}\cdot t^{69}-\frac{2603523798460517479542849}{144115188075855872}\cdot t^{67}+\frac{1020504533413493640741207}{144115188075855872}\cdot t^{65}-\frac{184042184782410101681391}{72057594037927936}\cdot t^{63}+\frac{7812778738911331707783261}{9223372036854775808}\cdot t^{61}-\frac{4760417122678958194082115}{18446744073709551616}\cdot t^{59}+\frac{2661443864505447597617637}{36893488147419103232}\cdot t^{57}-\frac{1363439456475198895964427}{73786976294838206464}\cdot t^{55}+\frac{10224470480151993794688519}{2361183241434822606848}\cdot t^{53}-\frac{4376357210508764929595901}{4722366482869645213696}\cdot t^{51}+\frac{213400092114123041681775}{1180591620717411303424}\cdot t^{49}-\frac{302776430800428591074145}{9444732965739290427392}\cdot t^{47}+\frac{1558375598415670931812545}{302231454903657293676544}\cdot t^{45}-\frac{453303479203119515785815}{604462909807314587353088}\cdot t^{43}+\frac{118838543451745303074735}{1208925819614629174706176}\cdot t^{41}-\frac{27974436759170715230725}{2417851639229258349412352}\cdot t^{39}+\frac{188421527256958400146105}{154742504910672534362390528}\cdot t^{37}-\frac{35294642082644781482555}{309485009821345068724781056}\cdot t^{35}+\frac{2926085074659307811355}{309485009821345068724781056}\cdot t^{33}-\frac{213425307787221241285}{309485009821345068724781056}\cdot t^{31}+\frac{870437583065595052025}{19807040628566084398385987584}\cdot t^{29}-\frac{96150142814337044119}{39614081257132168796771975168}\cdot t^{27}+\frac{9120085878082127949}{79228162514264337593543950336}\cdot t^{25}-\frac{734802695515287243}{158456325028528675187087900672}\cdot t^{23}+\frac{794362971420086937}{5070602400912917605986812821504}\cdot t^{21}-\frac{44324888101236435}{10141204801825835211973625643008}\cdot t^{19}+\frac{501228248924689}{5070602400912917605986812821504}\cdot t^{17}-\frac{35919991773333}{20282409603651670423947251286016}\cdot t^{15}+\frac{15844995797731}{649037107316853453566312041152512}\cdot t^{13}-\frac{323579219509}{1298074214633706907132624082305024}\cdot t^{11}+\frac{4648522385}{2596148429267413814265248164610048}\cdot t^9-\frac{43631043}{5192296858534827628530496329220096}\cdot t^7+\frac{30537759}{1329227995784915872903807060280344576}\cdot t^5-\frac{79453}{2658455991569831745807614120560689152}\cdot t^3+\frac{31}{2658455991569831745807614120560689152}\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.