Rule: Q[2, 8, 60, 71]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{10}-5\cdot t^8+\frac{35}{8}\cdot t^6-\frac{25}{16}\cdot t^4+\frac{25}{128}\cdot t^2-\frac{1}{256}$
• $P_3$:
  $2\cdot t^{70}-35\cdot t^{68}+\frac{2345}{8}\cdot t^{66}-\frac{25025}{16}\cdot t^{64}+\frac{47775}{8}\cdot t^{62}-\frac{277977}{16}\cdot t^{60}+\frac{82003215}{2048}\cdot t^{58}-\frac{307372595}{4096}\cdot t^{56}+\frac{3817369325}{32768}\cdot t^{54}-\frac{9950192175}{65536}\cdot t^{52}+\frac{87959698827}{524288}\cdot t^{50}-\frac{166025625675}{1048576}\cdot t^{48}+\frac{269076014025}{2097152}\cdot t^{46}-\frac{375834918375}{4194304}\cdot t^{44}+\frac{3627957477375}{67108864}\cdot t^{42}-\frac{3786268349115}{134217728}\cdot t^{40}+\frac{27345271410275}{2147483648}\cdot t^{38}-\frac{21335988680825}{4294967296}\cdot t^{36}+\frac{57443046448375}{34359738368}\cdot t^{34}-\frac{33256500575375}{68719476736}\cdot t^{32}+\frac{8247612142693}{68719476736}\cdot t^{30}-\frac{3486599885395}{137438953472}\cdot t^{28}+\frac{19968708434535}{4398046511104}\cdot t^{26}-\frac{6003543238875}{8796093022208}\cdot t^{24}+\frac{6003543238875}{70368744177664}\cdot t^{22}-\frac{1232727545049}{140737488355328}\cdot t^{20}+\frac{818944872585}{1125899906842624}\cdot t^{18}-\frac{107922967705}{2251799813685248}\cdot t^{16}+\frac{11012547725}{4503599627370496}\cdot t^{14}-\frac{842844275}{9007199254740992}\cdot t^{12}+\frac{370851481}{144115188075855872}\cdot t^{10}-\frac{13803405}{288230376151711744}\cdot t^8+\frac{5085465}{9223372036854775808}\cdot t^6-\frac{62475}{18446744073709551616}\cdot t^4+\frac{1225}{147573952589676412928}\cdot t^2-\frac{1}{295147905179352825856}$
• $P_4$:
  $2\cdot t^{141}-71\cdot t^{139}+\frac{2467}{2}\cdot t^{137}-\frac{55913}{4}\cdot t^{135}+\frac{14872995}{128}\cdot t^{133}-\frac{193395433}{256}\cdot t^{131}+\frac{1024001979}{256}\cdot t^{129}-\frac{1134976271}{64}\cdot t^{127}+\frac{137576127819}{2048}\cdot t^{125}-\frac{904246715125}{4096}\cdot t^{123}+\frac{5218365449075}{8192}\cdot t^{121}-\frac{26695906155325}{16384}\cdot t^{119}+\frac{31235490977023025}{8388608}\cdot t^{117}-\frac{128372222920262475}{16777216}\cdot t^{115}+\frac{14905657463096125}{1048576}\cdot t^{113}-\frac{804807938703795939}{33554432}\cdot t^{111}+\frac{79239579054126589813}{2147483648}\cdot t^{109}-\frac{223030526473987480611}{4294967296}\cdot t^{107}+\frac{575900613851763017499}{8589934592}\cdot t^{105}-\frac{1367593817419659480105}{17179869184}\cdot t^{103}+\frac{47888273732358063007185}{549755813888}\cdot t^{101}-\frac{96763197475923264368355}{1099511627776}\cdot t^{99}+\frac{90398808064402887759255}{1099511627776}\cdot t^{97}-\frac{78196601825551728859935}{1099511627776}\cdot t^{95}+\frac{2006392930298869875365925}{35184372088832}\cdot t^{93}-\frac{2985209459415300873186123}{70368744177664}\cdot t^{91}+\frac{4123883619043654658446233}{140737488355328}\cdot t^{89}-\frac{5292523024410500597817791}{281474976710656}\cdot t^{87}+\frac{202013440007064294621482393}{18014398509481984}\cdot t^{85}-\frac{224018236799429918226175795}{36028797018963968}\cdot t^{83}+\frac{57746711721770441807781407}{18014398509481984}\cdot t^{81}-\frac{110731181898407547171284289}{72057594037927936}\cdot t^{79}+\frac{6317186979477814209867841107}{9223372036854775808}\cdot t^{77}-\frac{5234270817256624839451135653}{18446744073709551616}\cdot t^{75}+\frac{4029862635823463219916797025}{36893488147419103232}\cdot t^{73}-\frac{2881470013895777645854409715}{73786976294838206464}\cdot t^{71}+\frac{30597115069535336150235587565}{2361183241434822606848}\cdot t^{69}-\frac{18833254448273945047935196455}{4722366482869645213696}\cdot t^{67}+\frac{5371012749251961637961828385}{4722366482869645213696}\cdot t^{65}-\frac{708972471352330168115465025}{2361183241434822606848}\cdot t^{63}+\frac{5537929575952526108912223129}{75557863725914323419136}\cdot t^{61}-\frac{2496521349207240100627438599}{151115727451828646838272}\cdot t^{59}+\frac{1037685481600158161758530153}{302231454903657293676544}\cdot t^{57}-\frac{397021701176438720871668727}{604462909807314587353088}\cdot t^{55}+\frac{8932079251510425827201880585}{77371252455336267181195264}\cdot t^{53}-\frac{2878866098757251705062524915}{154742504910672534362390528}\cdot t^{51}+\frac{106099117790384197899325035}{38685626227668133590597632}\cdot t^{49}-\frac{114170543794402077407480055}{309485009821345068724781056}\cdot t^{47}+\frac{894244881298737802469114115}{19807040628566084398385987584}\cdot t^{45}-\frac{198522605482375586139008325}{39614081257132168796771975168}\cdot t^{43}+\frac{39832813205506255644123381}{79228162514264337593543950336}\cdot t^{41}-\frac{7195325108377094325286551}{158456325028528675187087900672}\cdot t^{39}+\frac{18640534627209953748682107}{5070602400912917605986812821504}\cdot t^{37}-\frac{2692112684603509689032673}{10141204801825835211973625643008}\cdot t^{35}+\frac{172442278282146511226385}{10141204801825835211973625643008}\cdot t^{33}-\frac{9736924845904029959367}{10141204801825835211973625643008}\cdot t^{31}+\frac{15398669225408665675497}{324518553658426726783156020576256}\cdot t^{29}-\frac{1321332206869107740199}{649037107316853453566312041152512}\cdot t^{27}+\frac{97506379739387468421}{1298074214633706907132624082305024}\cdot t^{25}-\frac{6120303972198553475}{2596148429267413814265248164610048}\cdot t^{23}+\frac{10321860522351616095}{166153499473114484112975882535043072}\cdot t^{21}-\frac{449755084547613845}{332306998946228968225951765070086144}\cdot t^{19}+\frac{3975407304118635}{166153499473114484112975882535043072}\cdot t^{17}-\frac{222881991111755}{664613997892457936451903530140172288}\cdot t^{15}+\frac{615795335524025}{170141183460469231731687303715884105728}\cdot t^{13}-\frac{9851720603407}{340282366920938463463374607431768211456}\cdot t^{11}+\frac{110931484667}{680564733841876926926749214863536422912}\cdot t^9-\frac{816423249}{1361129467683753853853498429727072845824}\cdot t^7+\frac{56023331}{43556142965880123323311949751266331066368}\cdot t^5-\frac{114345}{87112285931760246646623899502532662132736}\cdot t^3+\frac{35}{87112285931760246646623899502532662132736}\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.