Rule: Q[10, 66, 77]

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.

• $P_1$:
  $1024\cdot t^{10}-2304\cdot t^8+1792\cdot t^6-560\cdot t^4+60\cdot t^2-1$
• $P_2$:
  $1024\cdot t^{76}-19200\cdot t^{74}+172864\cdot t^{72}-995136\cdot t^{70}+4115160\cdot t^{68}-13019909\cdot t^{66}+\frac{131115985}{4}\cdot t^{64}-67431078\cdot t^{62}+\frac{924001221}{8}\cdot t^{60}-\frac{5344712945}{32}\cdot t^{58}+\frac{26372568651}{128}\cdot t^{56}-\frac{27970906145}{128}\cdot t^{54}+\frac{205263418941}{1024}\cdot t^{52}-\frac{10468434365991}{65536}\cdot t^{50}+\frac{29078984349975}{262144}\cdot t^{48}-\frac{8817498480315}{131072}\cdot t^{46}+\frac{149608375854525}{4194304}\cdot t^{44}-\frac{277508869722315}{16777216}\cdot t^{42}+\frac{449972009097765}{67108864}\cdot t^{40}-\frac{159245992330425}{67108864}\cdot t^{38}+\frac{392806781081715}{536870912}\cdot t^{36}-\frac{841728816603675}{4294967296}\cdot t^{34}+\frac{780512175396135}{17179869184}\cdot t^{32}-\frac{38962765599485}{4294967296}\cdot t^{30}+\frac{106596245508025}{68719476736}\cdot t^{28}-\frac{61989816618513}{274877906944}\cdot t^{26}+\frac{30387165009075}{1099511627776}\cdot t^{24}-\frac{3106243534261}{1099511627776}\cdot t^{22}+\frac{2091959931237}{8796093022208}\cdot t^{20}-\frac{2284324062845}{140737488355328}\cdot t^{18}+\frac{495746924277}{562949953421312}\cdot t^{16}-\frac{10429458435}{281474976710656}\cdot t^{14}+\frac{21090682613}{18014398509481984}\cdot t^{12}-\frac{1917334783}{72057594037927936}\cdot t^{10}+\frac{118030185}{288230376151711744}\cdot t^8-\frac{1124097}{288230376151711744}\cdot t^6+\frac{45695}{2305843009213693952}\cdot t^4-\frac{741}{18446744073709551616}\cdot t^2+\frac{1}{73786976294838206464}$
• $P_3$:
  $1024\cdot t^{153}-38912\cdot t^{151}+724800\cdot t^{149}-8820800\cdot t^{147}+78880004\cdot t^{145}-552689424\cdot t^{143}+3159603447\cdot t^{141}-15153200205\cdot t^{139}+\frac{1990881413235}{32}\cdot t^{137}-\frac{3553074951283}{16}\cdot t^{135}+\frac{714168065207883}{1024}\cdot t^{133}-\frac{1992678727398219}{1024}\cdot t^{131}+\frac{79660372599980445}{16384}\cdot t^{129}-\frac{5606212801635285}{512}\cdot t^{127}+\frac{183082892350546593}{8192}\cdot t^{125}-\frac{340261970195859975}{8192}\cdot t^{123}+\frac{36999790759123730325}{524288}\cdot t^{121}-\frac{28834100570120038875}{262144}\cdot t^{119}+\frac{1323164837273286228375}{8388608}\cdot t^{117}-\frac{1750291732112382133675}{8388608}\cdot t^{115}+\frac{34248245683572133988775}{134217728}\cdot t^{113}-\frac{9699377850234714638425}{33554432}\cdot t^{111}+\frac{163125900208492928009875}{536870912}\cdot t^{109}-\frac{159336051879719444783625}{536870912}\cdot t^{107}+\frac{4633819231845584468553525}{17179869184}\cdot t^{105}-\frac{1961290930688131100643585}{8589934592}\cdot t^{103}+\frac{792512404531134820898519385}{4398046511104}\cdot t^{101}-\frac{583579417159847017430376625}{4398046511104}\cdot t^{99}+\frac{6419373588758317191734142875}{70368744177664}\cdot t^{97}-\frac{515320748780322842150244297}{8796093022208}\cdot t^{95}+\frac{4948187404955142989679227497}{140737488355328}\cdot t^{93}-\frac{2775812446682153384454200791}{140737488355328}\cdot t^{91}+\frac{186343474904318329661310692445}{18014398509481984}\cdot t^{89}-\frac{45687518640452703415583062335}{9007199254740992}\cdot t^{87}+\frac{670262773466406131285083279197}{288230376151711744}\cdot t^{85}-\frac{287255474342745484836464262513}{288230376151711744}\cdot t^{83}+\frac{1840923501296351948961370782169}{4611686018427387904}\cdot t^{81}-\frac{172227770391550598135679179205}{1152921504606846976}\cdot t^{79}+\frac{963037677997037010627999185355}{18446744073709551616}\cdot t^{77}-\frac{314141387493793789642979444409}{18446744073709551616}\cdot t^{75}+\frac{3058745088755360583365852485035}{590295810358705651712}\cdot t^{73}-\frac{433756858042795575927339754515}{295147905179352825856}\cdot t^{71}+\frac{7332556409771068069247886326325}{18889465931478580854784}\cdot t^{69}-\frac{1802029890773405163466953836325}{18889465931478580854784}\cdot t^{67}+\frac{6585600146280989779215594929115}{302231454903657293676544}\cdot t^{65}-\frac{87270949950716480254640911395}{18889465931478580854784}\cdot t^{63}+\frac{274460813613122843699377938735}{302231454903657293676544}\cdot t^{61}-\frac{49936696054087771323310959225}{302231454903657293676544}\cdot t^{59}+\frac{537369100305309287636383970025}{19342813113834066795298816}\cdot t^{57}-\frac{41673522064493373326903246655}{9671406556917033397649408}\cdot t^{55}+\frac{190415939279300490432157911639}{309485009821345068724781056}\cdot t^{53}-\frac{24975553429171528252000152507}{309485009821345068724781056}\cdot t^{51}+\frac{48029910440714477407692600975}{4951760157141521099596496896}\cdot t^{49}-\frac{1318960738797875617211061525}{1237940039285380274899124224}\cdot t^{47}+\frac{2112291197985931173637270383}{19807040628566084398385987584}\cdot t^{45}-\frac{192026472544175561239751853}{19807040628566084398385987584}\cdot t^{43}+\frac{505539080779564232651591613}{633825300114114700748351602688}\cdot t^{41}-\frac{18743988345055284444488385}{316912650057057350374175801344}\cdot t^{39}+\frac{159647073145815698544435555}{40564819207303340847894502572032}\cdot t^{37}-\frac{9484830572267016523692603}{40564819207303340847894502572032}\cdot t^{35}+\frac{8004927929785638059002977}{649037107316853453566312041152512}\cdot t^{33}-\frac{46564890125670025726617}{81129638414606681695789005144064}\cdot t^{31}+\frac{30368406603697842865185}{1298074214633706907132624082305024}\cdot t^{29}-\frac{1075315984746321664335}{1298074214633706907132624082305024}\cdot t^{27}+\frac{8387464681021308981813}{332306998946228968225951765070086144}\cdot t^{25}-\frac{108739818682212303135}{166153499473114484112975882535043072}\cdot t^{23}+\frac{75788358475481302185}{5316911983139663491615228241121378304}\cdot t^{21}-\frac{1365204604550615325}{5316911983139663491615228241121378304}\cdot t^{19}+\frac{319357027877093325}{85070591730234615865843651857942052864}\cdot t^{17}-\frac{925672544571285}{21267647932558653966460912964485513216}\cdot t^{15}+\frac{132238934938755}{340282366920938463463374607431768211456}\cdot t^{13}-\frac{875160098865}{340282366920938463463374607431768211456}\cdot t^{11}+\frac{130443917175}{10889035741470030830827987437816582766592}\cdot t^9-\frac{198544775}{5444517870735015415413993718908291383296}\cdot t^7+\frac{22537515}{348449143727040986586495598010130648530944}\cdot t^5-\frac{19019}{348449143727040986586495598010130648530944}\cdot t^3+\frac{77}{5575186299632655785383929568162090376495104}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.