Rule: Q[1, 28, 58, 88]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{29}-\frac{29}{4}\cdot t^{27}+\frac{377}{16}\cdot t^{25}-\frac{725}{16}\cdot t^{23}+\frac{7337}{128}\cdot t^{21}-\frac{51359}{1024}\cdot t^{19}+\frac{127281}{4096}\cdot t^{17}-\frac{28101}{2048}\cdot t^{15}+\frac{140505}{32768}\cdot t^{13}-\frac{121771}{131072}\cdot t^{11}+\frac{70499}{524288}\cdot t^9-\frac{6409}{524288}\cdot t^7+\frac{2639}{4194304}\cdot t^5-\frac{1015}{67108864}\cdot t^3+\frac{29}{268435456}\cdot t$
• $P_3$:
  $t^{87}-\frac{87}{4}\cdot t^{85}+\frac{1827}{8}\cdot t^{83}-\frac{98687}{64}\cdot t^{81}+\frac{481545}{64}\cdot t^{79}-\frac{7237269}{256}\cdot t^{77}+\frac{43572529}{512}\cdot t^{75}-\frac{3454679085}{16384}\cdot t^{73}+\frac{28730685555}{65536}\cdot t^{71}-\frac{203406705425}{262144}\cdot t^{69}+\frac{619730040165}{524288}\cdot t^{67}-\frac{6556091477535}{4194304}\cdot t^{65}+\frac{1893981982399}{1048576}\cdot t^{63}-\frac{7690118111487}{4194304}\cdot t^{61}+\frac{13769976657555}{8388608}\cdot t^{59}-\frac{174521704156123}{134217728}\cdot t^{57}+\frac{980762816313987}{1073741824}\cdot t^{55}-\frac{2447786188615581}{4294967296}\cdot t^{53}+\frac{2715820747111329}{8589934592}\cdot t^{51}-\frac{10720345054386825}{68719476736}\cdot t^{49}+\frac{4704151411924965}{68719476736}\cdot t^{47}-\frac{7337933154820905}{274877906944}\cdot t^{45}+\frac{5080107568722165}{549755813888}\cdot t^{43}-\frac{199449440632874565}{70368744177664}\cdot t^{41}+\frac{216334049363699925}{281474976710656}\cdot t^{39}-\frac{206843265262582767}{1125899906842624}\cdot t^{37}+\frac{86858521226280027}{2251799813685248}\cdot t^{35}-\frac{127606963283053373}{18014398509481984}\cdot t^{33}+\frac{10196198034723393}{9007199254740992}\cdot t^{31}-\frac{5637612468663945}{36028797018963968}\cdot t^{29}+\frac{1338520855133077}{72057594037927936}\cdot t^{27}-\frac{2165072903924931}{1152921504606846976}\cdot t^{25}+\frac{2952372141715815}{18446744073709551616}\cdot t^{23}-\frac{838327892092145}{73786976294838206464}\cdot t^{21}+\frac{97696369222725}{147573952589676412928}\cdot t^{19}-\frac{36716657444145}{1180591620717411303424}\cdot t^{17}+\frac{1359876201635}{1180591620717411303424}\cdot t^{15}-\frac{154364325591}{4722366482869645213696}\cdot t^{13}+\frac{6466389579}{9444732965739290427392}\cdot t^{11}-\frac{3039755785}{302231454903657293676544}\cdot t^9+\frac{116416179}{1208925819614629174706176}\cdot t^7-\frac{2592513}{4835703278458516698824704}\cdot t^5+\frac{13717}{9671406556917033397649408}\cdot t^3-\frac{87}{77371252455336267181195264}\cdot t$
• $P_4$:
  $t^{175}-44\cdot t^{173}+\frac{15223}{16}\cdot t^{171}-\frac{215645}{16}\cdot t^{169}+\frac{18006443}{128}\cdot t^{167}-\frac{73837547}{64}\cdot t^{165}+\frac{31712900703}{4096}\cdot t^{163}-\frac{179075242071}{4096}\cdot t^{161}+\frac{3473399931705}{16384}\cdot t^{159}-\frac{1836132550299}{2048}\cdot t^{157}+\frac{877416642801621}{262144}\cdot t^{155}-\frac{2920044441106611}{262144}\cdot t^{153}+\frac{69860174861678201}{2097152}\cdot t^{151}-\frac{94495278829543775}{1048576}\cdot t^{149}+\frac{59533511546828725165}{268435456}\cdot t^{147}-\frac{133922874827581602945}{268435456}\cdot t^{145}+\frac{4424249651286642901395}{4294967296}\cdot t^{143}-\frac{2103618079531470737235}{1073741824}\cdot t^{141}+\frac{236596526447127239371825}{68719476736}\cdot t^{139}-\frac{385237362407355362404115}{68719476736}\cdot t^{137}+\frac{4660565261557908401362685}{549755813888}\cdot t^{135}-\frac{3279803949566479013288505}{274877906944}\cdot t^{133}+\frac{275485411299774477563674815}{17592186044416}\cdot t^{131}-\frac{337691330473400456934155775}{17592186044416}\cdot t^{129}+\frac{387193920667675121469652911}{17592186044416}\cdot t^{127}-\frac{25987707725860186825705641}{1099511627776}\cdot t^{125}+\frac{6699093041626993306970621055}{281474976710656}\cdot t^{123}-\frac{6331568163017255475012306785}{281474976710656}\cdot t^{121}+\frac{44974716544656178390085336075}{2251799813685248}\cdot t^{119}-\frac{18772099083378100818654942305}{1125899906842624}\cdot t^{117}+\frac{1887097502511497783823411719195}{144115188075855872}\cdot t^{115}-\frac{1395117307734705731878479052495}{144115188075855872}\cdot t^{113}+\frac{31083525650086091970855653186755}{4611686018427387904}\cdot t^{111}-\frac{5097583113238504014652676367525}{1152921504606846976}\cdot t^{109}+\frac{201696801297848575706834519818365}{73786976294838206464}\cdot t^{107}-\frac{117548536905722548804153021279695}{73786976294838206464}\cdot t^{105}+\frac{516725248821061406514429152982585}{590295810358705651712}\cdot t^{103}-\frac{133861660414485564393954321213585}{295147905179352825856}\cdot t^{101}+\frac{4185491493369664068169130833763625}{18889465931478580854784}\cdot t^{99}-\frac{1928060998417450838950634839715425}{18889465931478580854784}\cdot t^{97}+\frac{3349425697251386834273684325096725}{75557863725914323419136}\cdot t^{95}-\frac{171398781319020818693843459071325}{9444732965739290427392}\cdot t^{93}+\frac{8464019577658196476277192193486825}{1208925819614629174706176}\cdot t^{91}-\frac{3076324990560382551798943235475375}{1208925819614629174706176}\cdot t^{89}+\frac{8423842772658001700755993222621725}{9671406556917033397649408}\cdot t^{87}-\frac{1357085269371621511065294826304275}{4835703278458516698824704}\cdot t^{85}+\frac{421258717846920313981569532574022725}{4951760157141521099596496896}\cdot t^{83}-\frac{120074465931172609841641290404518825}{4951760157141521099596496896}\cdot t^{81}+\frac{514570949335713353792121076878955125}{79228162514264337593543950336}\cdot t^{79}-\frac{32352829278799928497977976845501969}{19807040628566084398385987584}\cdot t^{77}+\frac{488558145553671625882511614873338447}{1267650600228229401496703205376}\cdot t^{75}-\frac{108055118202259424477944448527444989}{1267650600228229401496703205376}\cdot t^{73}+\frac{179035394995729842640125312944380419}{10141204801825835211973625643008}\cdot t^{71}-\frac{17342649093555076638252978035106255}{5070602400912917605986812821504}\cdot t^{69}+\frac{200904558679721339431240684184908701}{324518553658426726783156020576256}\cdot t^{67}-\frac{33932062619994578142705712690238733}{324518553658426726783156020576256}\cdot t^{65}+\frac{10680090455826813189034586909899281}{649037107316853453566312041152512}\cdot t^{63}-\frac{48866119369339999700972264016081}{20282409603651670423947251286016}\cdot t^{61}+\frac{3402391545700685313094976296169865}{10384593717069655257060992658440192}\cdot t^{59}-\frac{428968909985007843198922691060871}{10384593717069655257060992658440192}\cdot t^{57}+\frac{400344583405499209589710653387549}{83076749736557242056487941267521536}\cdot t^{55}-\frac{21560732027967205201208972535567}{41538374868278621028243970633760768}\cdot t^{53}+\frac{273813174594821325148000183837827}{5316911983139663491615228241121378304}\cdot t^{51}-\frac{24959872278127507993219583353575}{5316911983139663491615228241121378304}\cdot t^{49}+\frac{133413062969571293920746145684455}{340282366920938463463374607431768211456}\cdot t^{47}-\frac{2544283848563195847423761955285}{85070591730234615865843651857942052864}\cdot t^{45}+\frac{11307182310281291659658987827665}{5444517870735015415413993718908291383296}\cdot t^{43}-\frac{712073655563378439788215513755}{5444517870735015415413993718908291383296}\cdot t^{41}+\frac{324007700678520111639944771325}{43556142965880123323311949751266331066368}\cdot t^{39}-\frac{8284122360811646591539305645}{21778071482940061661655974875633165533184}\cdot t^{37}+\frac{24249940497453570261840163665}{1393796574908163946345982392040522594123776}\cdot t^{35}-\frac{986446227252773283256641465}{1393796574908163946345982392040522594123776}\cdot t^{33}+\frac{141832581140529353256946995}{5575186299632655785383929568162090376495104}\cdot t^{31}-\frac{559031244193066369788525}{696898287454081973172991196020261297061888}\cdot t^{29}+\frac{1962825563853006260954007}{89202980794122492566142873090593446023921664}\cdot t^{27}-\frac{46390996669988729588193}{89202980794122492566142873090593446023921664}\cdot t^{25}+\frac{7473888489473250997347}{713623846352979940529142984724747568191373312}\cdot t^{23}-\frac{63287219444593098357}{356811923176489970264571492362373784095686656}\cdot t^{21}+\frac{227169892631700948105}{91343852333181432387730302044767688728495783936}\cdot t^{19}-\frac{2587840575373799469}{91343852333181432387730302044767688728495783936}\cdot t^{17}+\frac{374386256739994707}{1461501637330902918203684832716283019655932542976}\cdot t^{15}-\frac{652262733055003}{365375409332725729550921208179070754913983135744}\cdot t^{13}+\frac{215792719675169}{23384026197294446691258957323460528314494920687616}\cdot t^{11}-\frac{785635893955}{23384026197294446691258957323460528314494920687616}\cdot t^9+\frac{14963504941}{187072209578355573530071658587684226515959365500928}\cdot t^7-\frac{10383769}{93536104789177786765035829293842113257979682750464}\cdot t^5+\frac{439031}{5986310706507378352962293074805895248510699696029696}\cdot t^3-\frac{87}{5986310706507378352962293074805895248510699696029696}\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.