Rule: Q[1, 36, 74]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{37}-\frac{37}{4}\cdot t^{35}+\frac{629}{16}\cdot t^{33}-\frac{407}{4}\cdot t^{31}+\frac{5735}{32}\cdot t^{29}-\frac{232841}{1024}\cdot t^{27}+\frac{878787}{4096}\cdot t^{25}-\frac{627705}{4096}\cdot t^{23}+\frac{5476185}{65536}\cdot t^{21}-\frac{9126975}{262144}\cdot t^{19}+\frac{11560835}{1048576}\cdot t^{17}-\frac{1374365}{524288}\cdot t^{15}+\frac{1924111}{4194304}\cdot t^{13}-\frac{1924111}{33554432}\cdot t^{11}+\frac{657305}{134217728}\cdot t^9-\frac{35853}{134217728}\cdot t^7+\frac{35853}{4294967296}\cdot t^5-\frac{2109}{17179869184}\cdot t^3+\frac{37}{68719476736}\cdot t$
• $P_3$:
  $t^{111}-\frac{111}{4}\cdot t^{109}+\frac{2997}{8}\cdot t^{107}-\frac{209827}{64}\cdot t^{105}+\frac{2676765}{128}\cdot t^{103}-\frac{53060553}{512}\cdot t^{101}+\frac{425326655}{1024}\cdot t^{99}-\frac{22673182455}{16384}\cdot t^{97}+\frac{64057243635}{16384}\cdot t^{95}-\frac{623127653225}{65536}\cdot t^{93}+\frac{2639346634155}{131072}\cdot t^{91}-\frac{39302270788599}{1048576}\cdot t^{89}+\frac{129551929636493}{2097152}\cdot t^{87}-\frac{760837941554349}{8388608}\cdot t^{85}+\frac{2000140980374835}{16777216}\cdot t^{83}-\frac{151255105693679189}{1073741824}\cdot t^{81}+\frac{644824397957263911}{4294967296}\cdot t^{79}-\frac{2486488072723817409}{17179869184}\cdot t^{77}+\frac{4346155376815943691}{34359738368}\cdot t^{75}-\frac{27598583914563486825}{274877906944}\cdot t^{73}+\frac{39851142048062001855}{549755813888}\cdot t^{71}-\frac{104793743904163041915}{2199023255552}\cdot t^{69}+\frac{125559817772812306605}{4398046511104}\cdot t^{67}-\frac{1097283624884142331635}{70368744177664}\cdot t^{65}+\frac{273269868266165714775}{35184372088832}\cdot t^{63}-\frac{496461444394252689261}{140737488355328}\cdot t^{61}+\frac{411097033140942272103}{281474976710656}\cdot t^{59}-\frac{1240541488014377826399}{2251799813685248}\cdot t^{57}+\frac{851938130323126941021}{4503599627370496}\cdot t^{55}-\frac{1064027017266478980165}{18014398509481984}\cdot t^{53}+\frac{603386514318192606859}{36028797018963968}\cdot t^{51}-\frac{4963340682294810153195}{1152921504606846976}\cdot t^{49}+\frac{9235583294903001171135}{9223372036854775808}\cdot t^{47}-\frac{7757315883286825381505}{36893488147419103232}\cdot t^{45}+\frac{2933438779394177665275}{73786976294838206464}\cdot t^{43}-\frac{3983301079387883356005}{590295810358705651712}\cdot t^{41}+\frac{1209743290777060871083}{1180591620717411303424}\cdot t^{39}-\frac{654798961625859828687}{4722366482869645213696}\cdot t^{37}+\frac{157208402466770961033}{9444732965739290427392}\cdot t^{35}-\frac{266492875976435104885}{151115727451828646838272}\cdot t^{33}+\frac{24772577203443263271}{151115727451828646838272}\cdot t^{31}-\frac{8027350801115761269}{604462909807314587353088}\cdot t^{29}+\frac{1124604701605589743}{1208925819614629174706176}\cdot t^{27}-\frac{539994870401589603}{9671406556917033397649408}\cdot t^{25}+\frac{54951988168411425}{19342813113834066795298816}\cdot t^{23}-\frac{9362190576840465}{77371252455336267181195264}\cdot t^{21}+\frac{657545157570735}{154742504910672534362390528}\cdot t^{19}-\frac{2392345147757355}{19807040628566084398385987584}\cdot t^{17}+\frac{215184484189815}{79228162514264337593543950336}\cdot t^{15}-\frac{14874503515425}{316912650057057350374175801344}\cdot t^{13}+\frac{380397139083}{633825300114114700748351602688}\cdot t^{11}-\frac{27348813921}{5070602400912917605986812821504}\cdot t^9+\frac{320911767}{10141204801825835211973625643008}\cdot t^7-\frac{4384611}{40564819207303340847894502572032}\cdot t^5+\frac{14245}{81129638414606681695789005144064}\cdot t^3-\frac{111}{1298074214633706907132624082305024}\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.