Rule: Q[4, 13, 48, 64]

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.

• $P_1$:
  $8\cdot t^4-8\cdot t^2+1$
• $P_2$:
  $8\cdot t^{17}-36\cdot t^{15}+67\cdot t^{13}-\frac{133}{2}\cdot t^{11}+\frac{605}{16}\cdot t^9-\frac{393}{32}\cdot t^7+\frac{273}{128}\cdot t^5-\frac{43}{256}\cdot t^3+\frac{1}{256}\cdot t$
• $P_3$:
  $8\cdot t^{65}-132\cdot t^{63}+1039\cdot t^{61}-\frac{10385}{2}\cdot t^{59}+\frac{296003}{16}\cdot t^{57}-\frac{1600655}{32}\cdot t^{55}+\frac{13654179}{128}\cdot t^{53}-\frac{47133801}{256}\cdot t^{51}+\frac{1072617975}{4096}\cdot t^{49}-\frac{2547050415}{8192}\cdot t^{47}+\frac{10192711165}{32768}\cdot t^{45}-\frac{17300015915}{65536}\cdot t^{43}+\frac{100092076315}{524288}\cdot t^{41}-\frac{123734259775}{1048576}\cdot t^{39}+\frac{261836368367}{4194304}\cdot t^{37}-\frac{237140973093}{8388608}\cdot t^{35}+\frac{2938136463237}{268435456}\cdot t^{33}-\frac{1940656365813}{536870912}\cdot t^{31}+\frac{2178666150595}{2147483648}\cdot t^{29}-\frac{1034046182477}{4294967296}\cdot t^{27}+\frac{1648973209611}{34359738368}\cdot t^{25}-\frac{547565693415}{68719476736}\cdot t^{23}+\frac{299711770995}{274877906944}\cdot t^{21}-\frac{66711441225}{549755813888}\cdot t^{19}+\frac{95017588965}{8796093022208}\cdot t^{17}-\frac{13247289117}{17592186044416}\cdot t^{15}+\frac{2814349167}{70368744177664}\cdot t^{13}-\frac{219631993}{140737488355328}\cdot t^{11}+\frac{47912205}{1125899906842624}\cdot t^9-\frac{1698521}{2251799813685248}\cdot t^7+\frac{69905}{9007199254740992}\cdot t^5-\frac{683}{18014398509481984}\cdot t^3+\frac{1}{18014398509481984}\cdot t$
• $P_4$:
  $8\cdot t^{129}-260\cdot t^{127}+4127\cdot t^{125}-\frac{85281}{2}\cdot t^{123}+\frac{5159563}{16}\cdot t^{121}-\frac{60900631}{32}\cdot t^{119}+\frac{1168118875}{128}\cdot t^{117}-\frac{9357607857}{256}\cdot t^{115}+\frac{511097362971}{4096}\cdot t^{113}-\frac{3019450971667}{8192}\cdot t^{111}+\frac{31239852500857}{32768}\cdot t^{109}-\frac{142855845216495}{65536}\cdot t^{107}+\frac{2327693219627463}{524288}\cdot t^{105}-\frac{8500109263067163}{1048576}\cdot t^{103}+\frac{55946938736077467}{4194304}\cdot t^{101}-\frac{166665345763105065}{8388608}\cdot t^{99}+\frac{7217816839718891175}{268435456}\cdot t^{97}-\frac{17807141912473374615}{536870912}\cdot t^{95}+\frac{80302260940473679905}{2147483648}\cdot t^{93}-\frac{165857736009128260335}{4294967296}\cdot t^{91}+\frac{1257601802367138238465}{34359738368}\cdot t^{89}-\frac{2191442234846618078325}{68719476736}\cdot t^{87}+\frac{7030179992337115482505}{274877906944}\cdot t^{85}-\frac{10391177851194886737355}{549755813888}\cdot t^{83}+\frac{113323343505707391936355}{8796093022208}\cdot t^{81}-\frac{142572050670428790295563}{17592186044416}\cdot t^{79}+\frac{331230106356859957643865}{70368744177664}\cdot t^{77}-\frac{355358096604105087043551}{140737488355328}\cdot t^{75}+\frac{1408569833573346912650259}{1125899906842624}\cdot t^{73}-\frac{1289192486728517088490983}{2251799813685248}\cdot t^{71}+\frac{2179084301700682107881727}{9007199254740992}\cdot t^{69}-\frac{1699870406241951648898725}{18014398509481984}\cdot t^{67}+\frac{39145380398283503935107429}{1152921504606846976}\cdot t^{65}-\frac{25968896537747586165726789}{2305843009213693952}\cdot t^{63}+\frac{31734097125697934484629931}{9223372036854775808}\cdot t^{61}-\frac{17839119683048991727585653}{18446744073709551616}\cdot t^{59}+\frac{36858721016206859808374895}{147573952589676412928}\cdot t^{57}-\frac{17469368051995931330821227}{295147905179352825856}\cdot t^{55}+\frac{15168921175879331591532879}{1180591620717411303424}\cdot t^{53}-\frac{6021385723142334664515693}{2361183241434822606848}\cdot t^{51}+\frac{17446210186256102244976515}{37778931862957161709568}\cdot t^{49}-\frac{5751120271856346366507675}{75557863725914323419136}\cdot t^{47}+\frac{3441973550529364107058305}{302231454903657293676544}\cdot t^{45}-\frac{932185764146718599526855}{604462909807314587353088}\cdot t^{43}+\frac{910888802376588902821815}{4835703278458516698824704}\cdot t^{41}-\frac{199956589604973575564715}{9671406556917033397649408}\cdot t^{39}+\frac{78552379563167357941275}{38685626227668133590597632}\cdot t^{37}-\frac{13740350032601371866505}{77371252455336267181195264}\cdot t^{35}+\frac{34060468121988709478805}{2475880078570760549798248448}\cdot t^{33}-\frac{4645243126878037054085}{4951760157141521099596496896}\cdot t^{31}+\frac{1107576850975242835891}{19807040628566084398385987584}\cdot t^{29}-\frac{114494882360893340765}{39614081257132168796771975168}\cdot t^{27}+\frac{40670856028090641339}{316912650057057350374175801344}\cdot t^{25}-\frac{3069124421574634839}{633825300114114700748351602688}\cdot t^{23}+\frac{388585495281704611}{2535301200456458802993406410752}\cdot t^{21}-\frac{20322043550690777}{5070602400912917605986812821504}\cdot t^{19}+\frac{6894138313266725}{81129638414606681695789005144064}\cdot t^{17}-\frac{231650227031901}{162259276829213363391578010288128}\cdot t^{15}+\frac{11980446908207}{649037107316853453566312041152512}\cdot t^{13}-\frac{229516303289}{1298074214633706907132624082305024}\cdot t^{11}+\frac{12374369293}{10384593717069655257060992658440192}\cdot t^9-\frac{108985305}{20769187434139310514121985316880384}\cdot t^7+\frac{1118481}{83076749736557242056487941267521536}\cdot t^5-\frac{2731}{166153499473114484112975882535043072}\cdot t^3+\frac{1}{166153499473114484112975882535043072}\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.