Rule: Q[19, 20, 38, 76]

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.

• $P_1$:
  $262144\cdot t^{19}-1245184\cdot t^{17}+2490368\cdot t^{15}-2723840\cdot t^{13}+1770496\cdot t^{11}-695552\cdot t^9+160512\cdot t^7-20064\cdot t^5+1140\cdot t^3-19\cdot t$
• $P_2$:
  $262144\cdot t^{39}-2621440\cdot t^{37}+12107776\cdot t^{35}-34258944\cdot t^{33}+66412544\cdot t^{31}-93454336\cdot t^{29}+98674240\cdot t^{27}-79694784\cdot t^{25}+49741380\cdot t^{23}-24075480\cdot t^{21}+\frac{36063885}{4}\cdot t^{19}-\frac{10367825}{4}\cdot t^{17}+\frac{9026235}{16}\cdot t^{15}-\frac{364021}{4}\cdot t^{13}+\frac{5400883}{512}\cdot t^{11}-\frac{429913}{512}\cdot t^9+\frac{702525}{16384}\cdot t^7-\frac{10317}{8192}\cdot t^5+\frac{4579}{262144}\cdot t^3-\frac{19}{262144}\cdot t$
• $P_3$:
  $262144\cdot t^{77}-5111808\cdot t^{75}+47906816\cdot t^{73}-287342592\cdot t^{71}+1239239680\cdot t^{69}-4093325824\cdot t^{67}+10770529792\cdot t^{65}-23183260672\cdot t^{63}+41600548704\cdot t^{61}-63103577680\cdot t^{59}+81767581272\cdot t^{57}-91228186196\cdot t^{55}+\frac{5642807573529}{64}\cdot t^{53}-\frac{9490989513891}{128}\cdot t^{51}+\frac{1742058970275}{32}\cdot t^{49}-\frac{8952821093895}{256}\cdot t^{47}+\frac{322489165730865}{16384}\cdot t^{45}-\frac{318199961380455}{32768}\cdot t^{43}+\frac{275130067799895}{65536}\cdot t^{41}-\frac{208244759201325}{131072}\cdot t^{39}+\frac{2203661208153405}{4194304}\cdot t^{37}-\frac{1270245305056455}{8388608}\cdot t^{35}+\frac{317986441828055}{8388608}\cdot t^{33}-\frac{68842914507185}{8388608}\cdot t^{31}+\frac{410268308308075}{268435456}\cdot t^{29}-\frac{130597282505669}{536870912}\cdot t^{27}+\frac{35249111410527}{1073741824}\cdot t^{25}-\frac{7990239579257}{2147483648}\cdot t^{23}+\frac{48115078418451}{137438953472}\cdot t^{21}-\frac{7410623527505}{274877906944}\cdot t^{19}+\frac{229488985407}{137438953472}\cdot t^{17}-\frac{44730788399}{549755813888}\cdot t^{15}+\frac{213414110077}{70368744177664}\cdot t^{13}-\frac{11726954603}{140737488355328}\cdot t^{11}+\frac{451512295}{281474976710656}\cdot t^9-\frac{11323221}{562949953421312}\cdot t^7+\frac{2641171}{18014398509481984}\cdot t^5-\frac{18297}{36028797018963968}\cdot t^3+\frac{19}{36028797018963968}\cdot t$
• $P_4$:
  $262144\cdot t^{153}-10092544\cdot t^{151}+190480384\cdot t^{149}-2349056000\cdot t^{147}+21288472576\cdot t^{145}-151178594304\cdot t^{143}+876018384384\cdot t^{141}-4258895317248\cdot t^{139}+17727235265740\cdot t^{137}-64154122546942\cdot t^{135}+\frac{408608518742499}{2}\cdot t^{133}-\frac{2312351291198193}{4}\cdot t^{131}+\frac{5859516768752361}{4}\cdot t^{129}-\frac{13384616997121035}{4}\cdot t^{127}+\frac{110850000613035561}{16}\cdot t^{125}-\frac{418011452436741975}{32}\cdot t^{123}+\frac{46118674355404117275}{2048}\cdot t^{121}-\frac{145879190291792492975}{4096}\cdot t^{119}+\frac{849195343324646385375}{16384}\cdot t^{117}-\frac{2280230806653870967325}{32768}\cdot t^{115}+\frac{11322443492108263025225}{131072}\cdot t^{113}-\frac{26042257392476135278325}{262144}\cdot t^{111}+\frac{111170827822652314884475}{1048576}\cdot t^{109}-\frac{220524136203237227992125}{2097152}\cdot t^{107}+\frac{104207051097550701885843225}{1073741824}\cdot t^{105}-\frac{179187863533656576069035565}{2147483648}\cdot t^{103}+\frac{574598732494077377331872385}{8589934592}\cdot t^{101}-\frac{859695849964620349106006251}{17179869184}\cdot t^{99}+\frac{1201044090799943216518000925}{34359738368}\cdot t^{97}-\frac{1567585986127187161316727931}{68719476736}\cdot t^{95}+\frac{3824408738016110115573749201}{274877906944}\cdot t^{93}-\frac{4361346286976416854019152767}{549755813888}\cdot t^{91}+\frac{297636216940836825172528758897}{70368744177664}\cdot t^{89}-\frac{296776906798907056640720228445}{140737488355328}\cdot t^{87}+\frac{553413088988001188300758833429}{562949953421312}\cdot t^{85}-\frac{482421079828400464393615847503}{1125899906842624}\cdot t^{83}+\frac{786176879863959320378728636417}{4503599627370496}\cdot t^{81}-\frac{598588331816630579607393513093}{9007199254740992}\cdot t^{79}+\frac{851381135620568951424752902995}{36028797018963968}\cdot t^{77}-\frac{565220391191674620116827943061}{72057594037927936}\cdot t^{75}+\frac{11202508877527534273085808658845}{4611686018427387904}\cdot t^{73}-\frac{6468392167492757192110792452465}{9223372036854775808}\cdot t^{71}+\frac{6957821340180802182662244961245}{36893488147419103232}\cdot t^{69}-\frac{3482321315197647842996607204975}{73786976294838206464}\cdot t^{67}+\frac{405026716437940587848461665705}{36893488147419103232}\cdot t^{65}-\frac{349899416157545514291971504565}{147573952589676412928}\cdot t^{63}+\frac{280268483800669086204037672935}{590295810358705651712}\cdot t^{61}-\frac{103920373225946177842814774265}{1180591620717411303424}\cdot t^{59}+\frac{1139694905043128489162880288075}{75557863725914323419136}\cdot t^{57}-\frac{360371704245533061801503131455}{151115727451828646838272}\cdot t^{55}+\frac{209845397389657441292930163807}{604462909807314587353088}\cdot t^{53}-\frac{56133174538831058546574600189}{1208925819614629174706176}\cdot t^{51}+\frac{27524467488203504478784631133}{4835703278458516698824704}\cdot t^{49}-\frac{6168472950135519300694156425}{9671406556917033397649408}\cdot t^{47}+\frac{2519857588691936446472662071}{38685626227668133590597632}\cdot t^{45}-\frac{467562038029401171939332673}{77371252455336267181195264}\cdot t^{43}+\frac{5025857596890994244196063699}{9903520314283042199192993792}\cdot t^{41}-\frac{761005926809244548446228431}{19807040628566084398385987584}\cdot t^{39}+\frac{206843968230356957688591195}{79228162514264337593543950336}\cdot t^{37}-\frac{25104096291593940554243817}{158456325028528675187087900672}\cdot t^{35}+\frac{2705733002914921139158089}{316912650057057350374175801344}\cdot t^{33}-\frac{257341655080566262579923}{633825300114114700748351602688}\cdot t^{31}+\frac{42886567860606746102409}{2535301200456458802993406410752}\cdot t^{29}-\frac{3105125933480951322855}{5070602400912917605986812821504}\cdot t^{27}+\frac{24768294578991424174077}{1298074214633706907132624082305024}\cdot t^{25}-\frac{1313854256449760565465}{2596148429267413814265248164610048}\cdot t^{23}+\frac{117116412816561723585}{10384593717069655257060992658440192}\cdot t^{21}-\frac{4318229940686638515}{20769187434139310514121985316880384}\cdot t^{19}+\frac{258527117805266025}{83076749736557242056487941267521536}\cdot t^{17}-\frac{6138754413482205}{166153499473114484112975882535043072}\cdot t^{15}+\frac{224569146344715}{664613997892457936451903530140172288}\cdot t^{13}-\frac{3045536062205}{1329227995784915872903807060280344576}\cdot t^{11}+\frac{930499942515}{85070591730234615865843651857942052864}\cdot t^9-\frac{5808062975}{170141183460469231731687303715884105728}\cdot t^7+\frac{42258755}{680564733841876926926749214863536422912}\cdot t^5-\frac{73169}{1361129467683753853853498429727072845824}\cdot t^3+\frac{19}{1361129467683753853853498429727072845824}\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.