Rule: Q[1, 58, 60]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{59}-\frac{59}{4}\cdot t^{57}+\frac{413}{4}\cdot t^{55}-\frac{29205}{64}\cdot t^{53}+\frac{365859}{256}\cdot t^{51}-\frac{3455335}{1024}\cdot t^{49}+\frac{3194555}{512}\cdot t^{47}-\frac{37948505}{4096}\cdot t^{45}+\frac{368323725}{32768}\cdot t^{43}-\frac{1478205883}{131072}\cdot t^{41}+\frac{1236866147}{131072}\cdot t^{39}-\frac{27773267119}{4194304}\cdot t^{37}+\frac{65592184047}{16777216}\cdot t^{35}-\frac{130526252535}{67108864}\cdot t^{33}+\frac{13674178837}{16777216}\cdot t^{31}-\frac{38536322177}{134217728}\cdot t^{29}+\frac{181927288417}{2147483648}\cdot t^{27}-\frac{178869686931}{8589934592}\cdot t^{25}+\frac{36355627425}{8589934592}\cdot t^{23}-\frac{96820776195}{137438953472}\cdot t^{21}+\frac{52134264105}{549755813888}\cdot t^{19}-\frac{22343256045}{2199023255552}\cdot t^{17}+\frac{933256395}{1099511627776}\cdot t^{15}-\frac{473390925}{8796093022208}\cdot t^{13}+\frac{175830915}{70368744177664}\cdot t^{11}-\frac{22754589}{281474976710656}\cdot t^9+\frac{477369}{281474976710656}\cdot t^7-\frac{371287}{18014398509481984}\cdot t^5+\frac{8555}{72057594037927936}\cdot t^3-\frac{59}{288230376151711744}\cdot t$
• $P_3$:
  $t^{119}-30\cdot t^{117}+\frac{7019}{16}\cdot t^{115}-\frac{66671}{16}\cdot t^{113}+\frac{1850149}{64}\cdot t^{111}-\frac{2498573}{16}\cdot t^{109}+\frac{2800858005}{4096}\cdot t^{107}-\frac{10219692087}{4096}\cdot t^{105}+\frac{507196030419}{65536}\cdot t^{103}-\frac{678878909007}{32768}\cdot t^{101}+\frac{50782956533335}{1048576}\cdot t^{99}-\frac{104635932357775}{1048576}\cdot t^{97}+\frac{382952360454755}{2097152}\cdot t^{95}-\frac{39140071753405}{131072}\cdot t^{93}+\frac{29436014785392985}{67108864}\cdot t^{91}-\frac{39004296983948415}{67108864}\cdot t^{89}+\frac{1497245348607271725}{2147483648}\cdot t^{87}-\frac{815433204657775935}{1073741824}\cdot t^{85}+\frac{25872719175099569003}{34359738368}\cdot t^{83}-\frac{23400396306069805463}{34359738368}\cdot t^{81}+\frac{77353526617131964347}{137438953472}\cdot t^{79}-\frac{14622740167419847125}{34359738368}\cdot t^{77}+\frac{5185457627209756508079}{17592186044416}\cdot t^{75}-\frac{3292354452686392466685}{17592186044416}\cdot t^{73}+\frac{30677557108066284540735}{281474976710656}\cdot t^{71}-\frac{8196003678645054343071}{140737488355328}\cdot t^{69}+\frac{128595827608665607231335}{4503599627370496}\cdot t^{67}-\frac{57851999979352105541223}{4503599627370496}\cdot t^{65}+\frac{23872014861368340948237}{4503599627370496}\cdot t^{63}-\frac{1128810976006076682429}{562949953421312}\cdot t^{61}+\frac{100141994909250552797697}{144115188075855872}\cdot t^{59}-\frac{31760927736985971578895}{144115188075855872}\cdot t^{57}+\frac{589339404847883602426017}{9223372036854775808}\cdot t^{55}-\frac{77989643072923618467207}{4611686018427387904}\cdot t^{53}+\frac{601985148301780940222019}{147573952589676412928}\cdot t^{51}-\frac{132086267259954572672055}{147573952589676412928}\cdot t^{49}+\frac{105224400633388383772425}{590295810358705651712}\cdot t^{47}-\frac{4743547403043074179645}{147573952589676412928}\cdot t^{45}+\frac{197702716587057871384195}{37778931862957161709568}\cdot t^{43}-\frac{28967865520845677062945}{37778931862957161709568}\cdot t^{41}+\frac{60898070769832834134905}{604462909807314587353088}\cdot t^{39}-\frac{3572933671160492185925}{302231454903657293676544}\cdot t^{37}+\frac{11925979507957116234045}{9671406556917033397649408}\cdot t^{35}-\frac{1099990860263675421909}{9671406556917033397649408}\cdot t^{33}+\frac{178351333505139630003}{19342813113834066795298816}\cdot t^{31}-\frac{394413448436818699}{604462909807314587353088}\cdot t^{29}+\frac{24751135131760072525}{618970019642690137449562112}\cdot t^{27}-\frac{1301528751911006619}{618970019642690137449562112}\cdot t^{25}+\frac{1859060180071991715}{19807040628566084398385987584}\cdot t^{23}-\frac{34773349130436345}{9903520314283042199192993792}\cdot t^{21}+\frac{34359322011094509}{316912650057057350374175801344}\cdot t^{19}-\frac{859613875179345}{316912650057057350374175801344}\cdot t^{17}+\frac{68118131742849}{1267650600228229401496703205376}\cdot t^{15}-\frac{259483944699}{316912650057057350374175801344}\cdot t^{13}+\frac{2998050817111}{324518553658426726783156020576256}\cdot t^{11}-\frac{23790638853}{324518553658426726783156020576256}\cdot t^9+\frac{1973133755}{5192296858534827628530496329220096}\cdot t^7-\frac{2978851}{2596148429267413814265248164610048}\cdot t^5+\frac{136939}{83076749736557242056487941267521536}\cdot t^3-\frac{59}{83076749736557242056487941267521536}\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.