Rule: Q[1, 6, 42, 98]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-\frac{7}{4}\cdot t^5+\frac{7}{8}\cdot t^3-\frac{7}{64}\cdot t$
• $P_3$:
  $t^{49}-\frac{49}{4}\cdot t^{47}+\frac{1127}{16}\cdot t^{45}-\frac{8085}{32}\cdot t^{43}+\frac{162239}{256}\cdot t^{41}-\frac{604709}{512}\cdot t^{39}+\frac{3473561}{2048}\cdot t^{37}-\frac{7868679}{4096}\cdot t^{35}+\frac{114191805}{65536}\cdot t^{33}-\frac{83740657}{65536}\cdot t^{31}+\frac{199689259}{262144}\cdot t^{29}-\frac{193956553}{524288}\cdot t^{27}+\frac{613322073}{4194304}\cdot t^{25}-\frac{393155175}{8388608}\cdot t^{23}+\frac{405992895}{33554432}\cdot t^{21}-\frac{167173545}{67108864}\cdot t^{19}+\frac{866262915}{2147483648}\cdot t^{17}-\frac{866262915}{17179869184}\cdot t^{15}+\frac{326012925}{68719476736}\cdot t^{13}-\frac{44612295}{137438953472}\cdot t^{11}+\frac{16921905}{1099511627776}\cdot t^9-\frac{1036035}{2199023255552}\cdot t^7+\frac{73255}{8796093022208}\cdot t^5-\frac{1225}{17592186044416}\cdot t^3+\frac{49}{281474976710656}\cdot t$
• $P_4$:
  $t^{147}-\frac{147}{4}\cdot t^{145}+\frac{1323}{2}\cdot t^{143}-\frac{497497}{64}\cdot t^{141}+\frac{17168865}{256}\cdot t^{139}-\frac{463849533}{1024}\cdot t^{137}+\frac{2553913859}{1024}\cdot t^{135}-\frac{94286330019}{8192}\cdot t^{133}+\frac{2977141744269}{65536}\cdot t^{131}-\frac{40821838892835}{262144}\cdot t^{129}+\frac{7687616375439}{16384}\cdot t^{127}-\frac{328923094223997}{262144}\cdot t^{125}+\frac{3147103679303675}{1048576}\cdot t^{123}-\frac{27109895414254275}{4194304}\cdot t^{121}+\frac{52851192456360375}{4194304}\cdot t^{119}-\frac{749632772194153925}{33554432}\cdot t^{117}+\frac{19416061038585986775}{536870912}\cdot t^{115}-\frac{115178534034326826525}{2147483648}\cdot t^{113}+\frac{78472196745178742275}{1073741824}\cdot t^{111}-\frac{25214355848911380083625}{274877906944}\cdot t^{109}+\frac{116859605139127860765525}{1099511627776}\cdot t^{107}-\frac{500915208423275962510425}{4398046511104}\cdot t^{105}+\frac{497272188725652137328531}{4398046511104}\cdot t^{103}-\frac{3663633670933871917793511}{35184372088832}\cdot t^{101}+\frac{25069579997582727892760475}{281474976710656}\cdot t^{99}-\frac{79745922995589385578872829}{1125899906842624}\cdot t^{97}+\frac{14752742270639867262207243}{281474976710656}\cdot t^{95}-\frac{162644430218288906977173679}{4503599627370496}\cdot t^{93}+\frac{417642780596542583462394357}{18014398509481984}\cdot t^{91}-\frac{999560015513057790343953765}{72057594037927936}\cdot t^{89}+\frac{557589319195033377063664237}{72057594037927936}\cdot t^{87}-\frac{2320291037940622762619764083}{576460752303423488}\cdot t^{85}+\frac{36014952197600101141532859897}{18446744073709551616}\cdot t^{83}-\frac{65156237282526924074766784811}{73786976294838206464}\cdot t^{81}+\frac{13736739250090267699261086855}{36893488147419103232}\cdot t^{79}-\frac{172746504610318835842544524899}{1180591620717411303424}\cdot t^{77}+\frac{252981117362258715553195835763}{4722366482869645213696}\cdot t^{75}-\frac{344974250948534612117994321495}{18889465931478580854784}\cdot t^{73}+\frac{109438958412934447204984195665}{18889465931478580854784}\cdot t^{71}-\frac{258267627403743685949084260425}{151115727451828646838272}\cdot t^{69}+\frac{566257807373067931996777266315}{1208925819614629174706176}\cdot t^{67}-\frac{576160152831041508350149349205}{4835703278458516698824704}\cdot t^{65}+\frac{16984312895246121561342271065}{604462909807314587353088}\cdot t^{63}-\frac{59338753281602281590879168855}{9671406556917033397649408}\cdot t^{61}+\frac{47921411520446679307726778025}{38685626227668133590597632}\cdot t^{59}-\frac{35727030549666347841185410545}{154742504910672534362390528}\cdot t^{57}+\frac{6136498144346479891792070085}{154742504910672534362390528}\cdot t^{55}-\frac{7755489144131508629201041767}{1237940039285380274899124224}\cdot t^{53}+\frac{17991690304062658065722282079}{19807040628566084398385987584}\cdot t^{51}-\frac{9554104597117821338523910725}{79228162514264337593543950336}\cdot t^{49}+\frac{579156031247966901757944279}{39614081257132168796771975168}\cdot t^{47}-\frac{4091945554111452423531619383}{2535301200456458802993406410752}\cdot t^{45}+\frac{1640091537882727894451944611}{10141204801825835211973625643008}\cdot t^{43}-\frac{594541412568487871814574863}{40564819207303340847894502572032}\cdot t^{41}+\frac{48538825000613306938266765}{40564819207303340847894502572032}\cdot t^{39}-\frac{28432623972691273076091441}{324518553658426726783156020576256}\cdot t^{37}+\frac{14863522422144731451080769}{2596148429267413814265248164610048}\cdot t^{35}-\frac{3447873622290883124129847}{10384593717069655257060992658440192}\cdot t^{33}+\frac{44083622446958211195771}{2596148429267413814265248164610048}\cdot t^{31}-\frac{31585338116849873969235}{41538374868278621028243970633760768}\cdot t^{29}+\frac{4913274818176647061881}{166153499473114484112975882535043072}\cdot t^{27}-\frac{657475966900496804697}{664613997892457936451903530140172288}\cdot t^{25}+\frac{18713737198306360665}{664613997892457936451903530140172288}\cdot t^{23}-\frac{3578666297181790815}{5316911983139663491615228241121378304}\cdot t^{21}+\frac{4527228448242024525}{340282366920938463463374607431768211456}\cdot t^{19}-\frac{290490080543859735}{1361129467683753853853498429727072845824}\cdot t^{17}+\frac{1847486483069815}{680564733841876926926749214863536422912}\cdot t^{15}-\frac{579062927529345}{21778071482940061661655974875633165533184}\cdot t^{13}+\frac{16815676972185}{87112285931760246646623899502532662132736}\cdot t^{11}-\frac{343687191925}{348449143727040986586495598010130648530944}\cdot t^9+\frac{1147749435}{348449143727040986586495598010130648530944}\cdot t^7-\frac{17867115}{2787593149816327892691964784081045188247552}\cdot t^5+\frac{132349}{22300745198530623141535718272648361505980416}\cdot t^3-\frac{147}{89202980794122492566142873090593446023921664}\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.