Rule: Q[26, 54, 81]

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.

• $P_1$:
  $67108864\cdot t^{26}-419430400\cdot t^{24}+1157627904\cdot t^{22}-1857028096\cdot t^{20}+1917583360\cdot t^{18}-1333592064\cdot t^{16}+635043840\cdot t^{14}-206389248\cdot t^{12}+44808192\cdot t^{10}-6223360\cdot t^8+512512\cdot t^6-21840\cdot t^4+364\cdot t^2-1$
• $P_2$:
  $67108864\cdot t^{80}-1325400064\cdot t^{78}+12595494912\cdot t^{76}-76703334400\cdot t^{74}+336324198400\cdot t^{72}-1131111383040\cdot t^{70}+3035148877824\cdot t^{68}-6673811914752\cdot t^{66}+12256272737280\cdot t^{64}-19065313146880\cdot t^{62}+25389089549824\cdot t^{60}-29180966560512\cdot t^{58}+29128102490656\cdot t^{56}-25371763481680\cdot t^{54}+19353408071580\cdot t^{52}-12960918738846\cdot t^{50}+\frac{122131734269895}{16}\cdot t^{48}-\frac{1012974972473835}{256}\cdot t^{46}+\frac{1849081298960175}{1024}\cdot t^{44}-\frac{1484915881847475}{2048}\cdot t^{42}+\frac{4191844505805495}{16384}\cdot t^{40}-\frac{2594951360736735}{32768}\cdot t^{38}+\frac{2810864108779545}{131072}\cdot t^{36}-\frac{1327469556620025}{262144}\cdot t^{34}+\frac{4355031703297275}{4194304}\cdot t^{32}-\frac{771462758869803}{4194304}\cdot t^{30}+\frac{469351468683027}{16777216}\cdot t^{28}-\frac{121683714103007}{33554432}\cdot t^{26}+\frac{106596245508025}{268435456}\cdot t^{24}-\frac{19509657665925}{536870912}\cdot t^{22}+\frac{5891151530495}{2147483648}\cdot t^{20}-\frac{722141155351}{4294967296}\cdot t^{18}+\frac{2254848913647}{274877906944}\cdot t^{16}-\frac{341643774795}{1099511627776}\cdot t^{14}+\frac{38910617655}{4398046511104}\cdot t^{12}-\frac{1595093643}{8796093022208}\cdot t^{10}+\frac{177232627}{70368744177664}\cdot t^8-\frac{3048227}{140737488355328}\cdot t^6+\frac{55965}{562949953421312}\cdot t^4-\frac{205}{1125899906842624}\cdot t^2+\frac{1}{18014398509481984}$
• $P_3$:
  $67108864\cdot t^{161}-2684354560\cdot t^{159}+52684652544\cdot t^{157}-676285382656\cdot t^{155}+6385653514240\cdot t^{153}-47294508957696\cdot t^{151}+286116620697600\cdot t^{149}-1453788875489280\cdot t^{147}+6331415756037120\cdot t^{145}-24001445349683200\cdot t^{143}+80160090340570240\cdot t^{141}-238163784365270400\cdot t^{139}+634508015513141224\cdot t^{137}-1525832904625819216\cdot t^{135}+3330395420448970755\cdot t^{133}-6629072789274617979\cdot t^{131}+\frac{773240476721553042345}{64}\cdot t^{129}-\frac{40465728802060990857}{2}\cdot t^{127}+\frac{3997114767225802319097}{128}\cdot t^{125}-\frac{5700706559808606546375}{128}\cdot t^{123}+\frac{120485637516180211035075}{2048}\cdot t^{121}-\frac{73853911547405296531125}{1024}\cdot t^{119}+\frac{1346826786946318407649425}{16384}\cdot t^{117}-\frac{1429397337537960074180325}{16384}\cdot t^{115}+\frac{45264249022035402349043625}{524288}\cdot t^{113}-\frac{10453728752242336717691535}{131072}\cdot t^{111}+\frac{288778344038187627427632675}{4194304}\cdot t^{109}-\frac{233161774075277417700829345}{4194304}\cdot t^{107}+\frac{2819318594415561270322821355}{67108864}\cdot t^{105}-\frac{997762478967394641947277975}{33554432}\cdot t^{103}+\frac{10588376367708533442725355965}{536870912}\cdot t^{101}-\frac{6583513993711905181699464125}{536870912}\cdot t^{99}+\frac{491332713592253108252678468775}{68719476736}\cdot t^{97}-\frac{33586520943233651515510790325}{8589934592}\cdot t^{95}+\frac{8821400941855191412750334047125}{4398046511104}\cdot t^{93}-\frac{4244989114652025743953422840675}{4398046511104}\cdot t^{91}+\frac{30658254716931297039663609404875}{70368744177664}\cdot t^{89}-\frac{6489606782243403200395821320513}{35184372088832}\cdot t^{87}+\frac{41218368374146980259220318438097}{562949953421312}\cdot t^{85}-\frac{15337666780873954505463470588285}{562949953421312}\cdot t^{83}+\frac{171128131328898580924892427580111}{18014398509481984}\cdot t^{81}-\frac{13970347346946971432086561816155}{4503599627370496}\cdot t^{79}+\frac{136643302145852758673837133192297}{144115188075855872}\cdot t^{77}-\frac{39067647261946958362287224127483}{144115188075855872}\cdot t^{75}+\frac{167045795303394159407314402085925}{2305843009213693952}\cdot t^{73}-\frac{20845030866919271173904190345765}{1152921504606846976}\cdot t^{71}+\frac{77661022045418873863795971528075}{18446744073709551616}\cdot t^{69}-\frac{16854094146027074753419551267795}{18446744073709551616}\cdot t^{67}+\frac{217920480449507966548600162883595}{1180591620717411303424}\cdot t^{65}-\frac{2558214056206974503460178903275}{73786976294838206464}\cdot t^{63}+\frac{28549668867269835458615596560549}{4722366482869645213696}\cdot t^{61}-\frac{4614546372293216648053925252235}{4722366482869645213696}\cdot t^{59}+\frac{11042641738452718440308064484719}{75557863725914323419136}\cdot t^{57}-\frac{762682024172171483067841047153}{37778931862957161709568}\cdot t^{55}+\frac{1553611530721090058101157688645}{604462909807314587353088}\cdot t^{53}-\frac{181892666893259311815071817753}{604462909807314587353088}\cdot t^{51}+\frac{625102830967400599903548699825}{19342813113834066795298816}\cdot t^{49}-\frac{15353402865865979646753827715}{4835703278458516698824704}\cdot t^{47}+\frac{44023948270560010605148243395}{154742504910672534362390528}\cdot t^{45}-\frac{3585955964115057635272071825}{154742504910672534362390528}\cdot t^{43}+\frac{4232834294896597443987818115}{2475880078570760549798248448}\cdot t^{41}-\frac{140842562969291101447411575}{1237940039285380274899124224}\cdot t^{39}+\frac{134663663432573814416170293}{19807040628566084398385987584}\cdot t^{37}-\frac{7189834844163392688886437}{19807040628566084398385987584}\cdot t^{35}+\frac{87305137393412625507906735}{5070602400912917605986812821504}\cdot t^{33}-\frac{456949965738717944767791}{633825300114114700748351602688}\cdot t^{31}+\frac{2146280142106099437545685}{81129638414606681695789005144064}\cdot t^{29}-\frac{68451668318544883868307}{81129638414606681695789005144064}\cdot t^{27}+\frac{30070757922164273138643}{1298074214633706907132624082305024}\cdot t^{25}-\frac{351458133732635263425}{649037107316853453566312041152512}\cdot t^{23}+\frac{110458270601685368505}{10384593717069655257060992658440192}\cdot t^{21}-\frac{1795096488651441525}{10384593717069655257060992658440192}\cdot t^{19}+\frac{757929628541719755}{332306998946228968225951765070086144}\cdot t^{17}-\frac{1983192809790555}{83076749736557242056487941267521536}\cdot t^{15}+\frac{511634508668325}{2658455991569831745807614120560689152}\cdot t^{13}-\frac{3058045339167}{2658455991569831745807614120560689152}\cdot t^{11}+\frac{205865965305}{42535295865117307932921825928971026432}\cdot t^9-\frac{283085361}{21267647932558653966460912964485513216}\cdot t^7+\frac{7258599}{340282366920938463463374607431768211456}\cdot t^5-\frac{5535}{340282366920938463463374607431768211456}\cdot t^3+\frac{81}{21778071482940061661655974875633165533184}\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.