Rule: Q[1, 52, 54]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{53}-\frac{53}{4}\cdot t^{51}+\frac{1325}{16}\cdot t^{49}-\frac{2597}{8}\cdot t^{47}+\frac{57293}{64}\cdot t^{45}-\frac{1890669}{1024}\cdot t^{43}+\frac{12108327}{4096}\cdot t^{41}-\frac{15417435}{4096}\cdot t^{39}+\frac{253873763}{65536}\cdot t^{37}-\frac{853939021}{262144}\cdot t^{35}+\frac{2363226593}{1048576}\cdot t^{33}-\frac{337603799}{262144}\cdot t^{31}+\frac{1276307045}{2097152}\cdot t^{29}-\frac{3986005079}{16777216}\cdot t^{27}+\frac{5124863673}{67108864}\cdot t^{25}-\frac{1348648335}{67108864}\cdot t^{23}+\frac{9221838615}{2147483648}\cdot t^{21}-\frac{6328712775}{8589934592}\cdot t^{19}+\frac{3435586935}{34359738368}\cdot t^{17}-\frac{180820365}{17179869184}\cdot t^{15}+\frac{115067505}{137438953472}\cdot t^{13}-\frac{213696795}{4398046511104}\cdot t^{11}+\frac{34467225}{17592186044416}\cdot t^9-\frac{899145}{17592186044416}\cdot t^7+\frac{217035}{281474976710656}\cdot t^5-\frac{6201}{1125899906842624}\cdot t^3+\frac{53}{4503599627370496}\cdot t$
• $P_3$:
  $t^{107}-27\cdot t^{105}+\frac{5669}{16}\cdot t^{103}-\frac{24089}{8}\cdot t^{101}+\frac{4769725}{256}\cdot t^{99}-\frac{22904805}{256}\cdot t^{97}+\frac{177709917}{512}\cdot t^{95}-\frac{35774473}{32}\cdot t^{93}+\frac{49964465357}{16384}\cdot t^{91}-\frac{117164006635}{16384}\cdot t^{89}+\frac{15291107200941}{1048576}\cdot t^{87}-\frac{13682757680527}{524288}\cdot t^{85}+\frac{692749143671767}{16777216}\cdot t^{83}-\frac{974776160492659}{16777216}\cdot t^{81}+\frac{4903286589564435}{67108864}\cdot t^{79}-\frac{1383182736366789}{16777216}\cdot t^{77}+\frac{359686855929202659}{4294967296}\cdot t^{75}-\frac{329793298428111705}{4294967296}\cdot t^{73}+\frac{4376482318842024285}{68719476736}\cdot t^{71}-\frac{1644530354842301325}{34359738368}\cdot t^{69}+\frac{35882656838676870705}{1099511627776}\cdot t^{67}-\frac{22219191845139690225}{1099511627776}\cdot t^{65}+\frac{12502093947297425055}{1099511627776}\cdot t^{63}-\frac{799249187853714195}{137438953472}\cdot t^{61}+\frac{95113304080842039525}{35184372088832}\cdot t^{59}-\frac{40175319664630529899}{35184372088832}\cdot t^{57}+\frac{493141950043482913271}{1125899906842624}\cdot t^{55}-\frac{85816463618805690001}{562949953421312}\cdot t^{53}+\frac{866184135623123990409}{18014398509481984}\cdot t^{51}-\frac{247243408893172879525}{18014398509481984}\cdot t^{49}+\frac{255005889694781702855}{72057594037927936}\cdot t^{47}-\frac{14817876306217467707}{18014398509481984}\cdot t^{45}+\frac{1585632057616497937431}{9223372036854775808}\cdot t^{43}-\frac{297129894809849925117}{9223372036854775808}\cdot t^{41}+\frac{796089211382705186135}{147573952589676412928}\cdot t^{39}-\frac{59335760301680911867}{73786976294838206464}\cdot t^{37}+\frac{250860982340037751591}{2361183241434822606848}\cdot t^{35}-\frac{29227535461342685103}{2361183241434822606848}\cdot t^{33}+\frac{5971129881901821637}{4722366482869645213696}\cdot t^{31}-\frac{2075023382719595}{18446744073709551616}\cdot t^{29}+\frac{1306856586018231409}{151115727451828646838272}\cdot t^{27}-\frac{86046003889891479}{151115727451828646838272}\cdot t^{25}+\frac{614505145770361755}{19342813113834066795298816}\cdot t^{23}-\frac{14344978077196305}{9671406556917033397649408}\cdot t^{21}+\frac{17665162087010025}{309485009821345068724781056}\cdot t^{19}-\frac{550128576835005}{309485009821345068724781056}\cdot t^{17}+\frac{54205933280625}{1237940039285380274899124224}\cdot t^{15}-\frac{256518713955}{309485009821345068724781056}\cdot t^{13}+\frac{919765609035}{79228162514264337593543950336}\cdot t^{11}-\frac{9054441825}{79228162514264337593543950336}\cdot t^9+\frac{931148361}{1267650600228229401496703205376}\cdot t^7-\frac{1742481}{633825300114114700748351602688}\cdot t^5+\frac{99269}{20282409603651670423947251286016}\cdot t^3-\frac{53}{20282409603651670423947251286016}\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.