Rule: Q[1, 72, 74]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{73}-\frac{73}{4}\cdot t^{71}+\frac{2555}{16}\cdot t^{69}-\frac{28543}{32}\cdot t^{67}+\frac{914617}{256}\cdot t^{65}-\frac{699413}{64}\cdot t^{63}+\frac{6795789}{256}\cdot t^{61}-\frac{26918385}{512}\cdot t^{59}+\frac{708574719}{8192}\cdot t^{57}-\frac{31413479209}{262144}\cdot t^{55}+\frac{148092116271}{1048576}\cdot t^{53}-\frac{299224246659}{2097152}\cdot t^{51}+\frac{2084759095575}{16777216}\cdot t^{49}-\frac{1571587625895}{16777216}\cdot t^{47}+\frac{4113525965115}{67108864}\cdot t^{45}-\frac{4680908856855}{134217728}\cdot t^{43}+\frac{74155450837545}{4294967296}\cdot t^{41}-\frac{127746785056275}{17179869184}\cdot t^{39}+\frac{191233066114545}{68719476736}\cdot t^{37}-\frac{124133744670845}{137438953472}\cdot t^{35}+\frac{278715388977935}{1099511627776}\cdot t^{33}-\frac{33690871195135}{549755813888}\cdot t^{31}+\frac{27925588423775}{2199023255552}\cdot t^{29}-\frac{9858946869611}{4398046511104}\cdot t^{27}+\frac{23540750688663}{70368744177664}\cdot t^{25}-\frac{23540750688663}{562949953421312}\cdot t^{23}+\frac{9747643083849}{2251799813685248}\cdot t^{21}-\frac{1648152212245}{4503599627370496}\cdot t^{19}+\frac{894711200933}{36028797018963968}\cdot t^{17}-\frac{47680534219}{36028797018963968}\cdot t^{15}+\frac{7761947431}{144115188075855872}\cdot t^{13}-\frac{465001459}{288230376151711744}\cdot t^{11}+\frac{623782445}{18446744073709551616}\cdot t^9-\frac{34024497}{73786976294838206464}\cdot t^7+\frac{1077699}{295147905179352825856}\cdot t^5-\frac{8103}{590295810358705651712}\cdot t^3+\frac{73}{4722366482869645213696}\cdot t$
• $P_3$:
  $t^{147}-37\cdot t^{145}+\frac{10729}{16}\cdot t^{143}-\frac{31737}{4}\cdot t^{141}+\frac{17645915}{256}\cdot t^{139}-\frac{120018577}{256}\cdot t^{137}+\frac{5323756295}{2048}\cdot t^{135}-\frac{12371245083}{1024}\cdot t^{133}+\frac{3147381536409}{65536}\cdot t^{131}-\frac{10866769864665}{65536}\cdot t^{129}+\frac{32980766370981}{65536}\cdot t^{127}-\frac{5552493654071}{4096}\cdot t^{125}+\frac{3425099435318925}{1048576}\cdot t^{123}-\frac{7430920644723475}{1048576}\cdot t^{121}+\frac{116760715224657625}{8388608}\cdot t^{119}-\frac{104287593950674475}{4194304}\cdot t^{117}+\frac{21773217585394960575}{536870912}\cdot t^{115}-\frac{32537647356530549475}{536870912}\cdot t^{113}+\frac{5718861521980271197225}{68719476736}\cdot t^{111}-\frac{1808453719090060417375}{17179869184}\cdot t^{109}+\frac{135156379510333497101775}{1099511627776}\cdot t^{107}-\frac{145981003597640423360181}{1099511627776}\cdot t^{105}+\frac{1168595099640774355639947}{8796093022208}\cdot t^{103}-\frac{542422838177643665943987}{4398046511104}\cdot t^{101}+\frac{29934202412637255218889975}{281474976710656}\cdot t^{99}-\frac{23999546061471298195519551}{281474976710656}\cdot t^{97}+\frac{71622723812789015438516343}{1125899906842624}\cdot t^{95}-\frac{6220152278970747085561607}{140737488355328}\cdot t^{93}+\frac{515396135215588063046005627}{18014398509481984}\cdot t^{91}-\frac{310985850515167872325745485}{18014398509481984}\cdot t^{89}+\frac{1399662984918145007731238799}{144115188075855872}\cdot t^{87}-\frac{367156375420950363206617505}{72057594037927936}\cdot t^{85}+\frac{45986868786504771704649727657}{18446744073709551616}\cdot t^{83}-\frac{20981320403602222435490189149}{18446744073709551616}\cdot t^{81}+\frac{142800680037138574906701502515}{295147905179352825856}\cdot t^{79}-\frac{14154689995954911045013300839}{73786976294838206464}\cdot t^{77}+\frac{334648491056197521687251634321}{4722366482869645213696}\cdot t^{75}-\frac{115120596631206051987450267555}{4722366482869645213696}\cdot t^{73}+\frac{294842726709374664641697154005}{37778931862957161709568}\cdot t^{71}-\frac{43890226209562392557816913225}{18889465931478580854784}\cdot t^{69}+\frac{777032758134446060964901264815}{1208925819614629174706176}\cdot t^{67}-\frac{199519016318880263176647118335}{1208925819614629174706176}\cdot t^{65}+\frac{95000167732750284337617757935}{2417851639229258349412352}\cdot t^{63}-\frac{654485951920453142175339885}{75557863725914323419136}\cdot t^{61}+\frac{68312141512473477625940519775}{38685626227668133590597632}\cdot t^{59}-\frac{12857110812074311073984889105}{38685626227668133590597632}\cdot t^{57}+\frac{17841763992474051059536943907}{309485009821345068724781056}\cdot t^{55}-\frac{1423411771042071019624543569}{154742504910672534362390528}\cdot t^{53}+\frac{26684052133597303361947957719}{19807040628566084398385987584}\cdot t^{51}-\frac{3578685227099115209275279275}{19807040628566084398385987584}\cdot t^{49}+\frac{14027132811246109926704314839}{633825300114114700748351602688}\cdot t^{47}-\frac{391174172197550231680251477}{158456325028528675187087900672}\cdot t^{45}+\frac{2535032209154675233008006441}{10141204801825835211973625643008}\cdot t^{43}-\frac{232189057252809359053325667}{10141204801825835211973625643008}\cdot t^{41}+\frac{153282766794305908955893005}{81129638414606681695789005144064}\cdot t^{39}-\frac{5672921685214398433138077}{40564819207303340847894502572032}\cdot t^{37}+\frac{23986107612455783558622405}{2596148429267413814265248164610048}\cdot t^{35}-\frac{1406504740668534986889933}{2596148429267413814265248164610048}\cdot t^{33}+\frac{290973718229056888121499}{10384593717069655257060992658440192}\cdot t^{31}-\frac{1647307883645231522205}{1298074214633706907132624082305024}\cdot t^{29}+\frac{8294503335668881632231}{166153499473114484112975882535043072}\cdot t^{27}-\frac{280723031885886390801}{166153499473114484112975882535043072}\cdot t^{25}+\frac{64676664129812297355}{1329227995784915872903807060280344576}\cdot t^{23}-\frac{782255799900322605}{664613997892457936451903530140172288}\cdot t^{21}+\frac{8012600938675572525}{340282366920938463463374607431768211456}\cdot t^{19}-\frac{130106962252490465}{340282366920938463463374607431768211456}\cdot t^{17}+\frac{26807405907400785}{5444517870735015415413993718908291383296}\cdot t^{15}-\frac{66467827641145}{1361129467683753853853498429727072845824}\cdot t^{13}+\frac{31276044576035}{87112285931760246646623899502532662132736}\cdot t^{11}-\frac{161869106825}{87112285931760246646623899502532662132736}\cdot t^9+\frac{4381008495}{696898287454081973172991196020261297061888}\cdot t^7-\frac{4318899}{348449143727040986586495598010130648530944}\cdot t^5+\frac{259369}{22300745198530623141535718272648361505980416}\cdot t^3-\frac{73}{22300745198530623141535718272648361505980416}\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.