Rule: Q[4, 70, 75]

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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{74}-292\cdot t^{72}+2556\cdot t^{70}-\frac{57155}{4}\cdot t^{68}+\frac{916895}{16}\cdot t^{66}-\frac{11238513}{64}\cdot t^{64}+\frac{3420417}{8}\cdot t^{62}-\frac{54353013}{64}\cdot t^{60}+\frac{717946515}{512}\cdot t^{58}-\frac{3995843735}{2048}\cdot t^{56}+\frac{4733537963}{2048}\cdot t^{54}-\frac{615790256823}{262144}\cdot t^{52}+\frac{2160153123141}{1048576}\cdot t^{50}-\frac{6566222272575}{4194304}\cdot t^{48}+\frac{2168237331225}{2097152}\cdot t^{46}-\frac{9973891723635}{16777216}\cdot t^{44}+\frac{79960182801345}{268435456}\cdot t^{42}-\frac{139646485582065}{1073741824}\cdot t^{40}+\frac{53081997443475}{1073741824}\cdot t^{38}-\frac{280576272201225}{17179869184}\cdot t^{36}+\frac{321387366339585}{68719476736}\cdot t^{34}-\frac{317986441828055}{274877906944}\cdot t^{32}+\frac{16908369977135}{68719476736}\cdot t^{30}-\frac{24599133578775}{549755813888}\cdot t^{28}+\frac{30387165009075}{4398046511104}\cdot t^{26}-\frac{15801325804719}{17592186044416}\cdot t^{24}+\frac{1711603580103}{17592186044416}\cdot t^{22}-\frac{4881239839553}{562949953421312}\cdot t^{20}+\frac{1409476549415}{2251799813685248}\cdot t^{18}-\frac{323313211485}{9007199254740992}\cdot t^{16}+\frac{7184738033}{4503599627370496}\cdot t^{14}-\frac{1917334783}{36028797018963968}\cdot t^{12}+\frac{1471442973}{1152921504606846976}\cdot t^{10}-\frac{95548245}{4611686018427387904}\cdot t^8+\frac{959595}{4611686018427387904}\cdot t^6-\frac{82251}{73786976294838206464}\cdot t^4+\frac{703}{295147905179352825856}\cdot t^2-\frac{1}{1180591620717411303424}$
• $P_3$:
  $16\cdot t^{149}-592\cdot t^{147}+10731\cdot t^{145}-127020\cdot t^{143}+\frac{4416555}{4}\cdot t^{141}-\frac{30063033}{4}\cdot t^{139}+\frac{10679057389}{256}\cdot t^{137}-\frac{24846677981}{128}\cdot t^{135}+\frac{3165326793495}{4096}\cdot t^{133}-\frac{10947690541095}{4096}\cdot t^{131}+\frac{532683342613851}{65536}\cdot t^{129}-\frac{44941890907251}{2048}\cdot t^{127}+\frac{1737101783328093}{32768}\cdot t^{125}-\frac{3779488720042875}{32768}\cdot t^{123}+\frac{238298351819173875}{1048576}\cdot t^{121}-\frac{213585930149037325}{524288}\cdot t^{119}+\frac{22381892769796881475}{33554432}\cdot t^{117}-\frac{33587687823052109175}{33554432}\cdot t^{115}+\frac{741304019124937965125}{536870912}\cdot t^{113}-\frac{235585166383216524875}{134217728}\cdot t^{111}+\frac{4425376740829344259575}{2147483648}\cdot t^{109}-\frac{4807635196847825823525}{2147483648}\cdot t^{107}+\frac{2478554472847638204110025}{1099511627776}\cdot t^{105}-\frac{1158242675603227027939125}{549755813888}\cdot t^{103}+\frac{32191792460019849617800125}{17592186044416}\cdot t^{101}-\frac{26010968307696038491182501}{17592186044416}\cdot t^{99}+\frac{313099769877502438512968517}{281474976710656}\cdot t^{97}-\frac{27435119853764892986231207}{35184372088832}\cdot t^{95}+\frac{286880117440422124551574565}{562949953421312}\cdot t^{93}-\frac{174875055914808470907899115}{562949953421312}\cdot t^{91}+\frac{3182726017649514170523763893}{18014398509481984}\cdot t^{89}-\frac{844643201756268466506577623}{9007199254740992}\cdot t^{87}+\frac{53556105385935598867815370977}{1152921504606846976}\cdot t^{85}-\frac{24759815621314437705011768245}{1152921504606846976}\cdot t^{83}+\frac{170908017361730287038854051395}{18446744073709551616}\cdot t^{81}-\frac{17196955784223792857325687159}{4611686018427387904}\cdot t^{79}+\frac{103282301698232954763002811183}{73786976294838206464}\cdot t^{77}-\frac{36140159623179816507599405109}{73786976294838206464}\cdot t^{75}+\frac{754052202664090156455551497575}{4722366482869645213696}\cdot t^{73}-\frac{114440355082076052850842534975}{2361183241434822606848}\cdot t^{71}+\frac{1034124663196214513943067997865}{75557863725914323419136}\cdot t^{69}-\frac{271431691637762279000944005705}{75557863725914323419136}\cdot t^{67}+\frac{1058439982735612696421670540765}{1208925819614629174706176}\cdot t^{65}-\frac{14952966502459210012477414725}{75557863725914323419136}\cdot t^{63}+\frac{50091155367586341602690207475}{1208925819614629174706176}\cdot t^{61}-\frac{9700191991818307421473341765}{1208925819614629174706176}\cdot t^{59}+\frac{55508456515053926415186915585}{38685626227668133590597632}\cdot t^{57}-\frac{4575061794981722090406853815}{19342813113834066795298816}\cdot t^{55}+\frac{44405011539528479112772404675}{1237940039285380274899124224}\cdot t^{53}-\frac{6182067680488002042574295175}{1237940039285380274899124224}\cdot t^{51}+\frac{12611418068195524166851562157}{19807040628566084398385987584}\cdot t^{49}-\frac{367177353144135878892291471}{4951760157141521099596496896}\cdot t^{47}+\frac{623106308867834984431031523}{79228162514264337593543950336}\cdot t^{45}-\frac{59995647323395899103940985}{79228162514264337593543950336}\cdot t^{43}+\frac{668840364605265393714305055}{10141204801825835211973625643008}\cdot t^{41}-\frac{26241583683077398222283739}{5070602400912917605986812821504}\cdot t^{39}+\frac{59103384526323258610067631}{162259276829213363391578010288128}\cdot t^{37}-\frac{3712776277544924564639223}{162259276829213363391578010288128}\cdot t^{35}+\frac{3311996829294198074903055}{2596148429267413814265248164610048}\cdot t^{33}-\frac{20356843987094158404135}{324518553658426726783156020576256}\cdot t^{31}+\frac{14023603635553753567293}{5192296858534827628530496329220096}\cdot t^{29}-\frac{524367570089779328451}{5192296858534827628530496329220096}\cdot t^{27}+\frac{539744918186253795561}{166153499473114484112975882535043072}\cdot t^{25}-\frac{7385672115301776075}{83076749736557242056487941267521536}\cdot t^{23}+\frac{43455233608636031325}{21267647932558653966460912964485513216}\cdot t^{21}-\frac{825846068580413265}{21267647932558653966460912964485513216}\cdot t^{19}+\frac{203780198740621455}{340282366920938463463374607431768211456}\cdot t^{17}-\frac{622956910374135}{85070591730234615865843651857942052864}\cdot t^{15}+\frac{93845732552775}{1361129467683753853853498429727072845824}\cdot t^{13}-\frac{654854816525}{1361129467683753853853498429727072845824}\cdot t^{11}+\frac{205811513765}{87112285931760246646623899502532662132736}\cdot t^9-\frac{330237765}{43556142965880123323311949751266331066368}\cdot t^7+\frac{19757815}{1393796574908163946345982392040522594123776}\cdot t^5-\frac{17575}{1393796574908163946345982392040522594123776}\cdot t^3+\frac{75}{22300745198530623141535718272648361505980416}\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.