Rule: Q[7, 42, 50]

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.

• $P_1$:
  $64\cdot t^7-112\cdot t^5+56\cdot t^3-7\cdot t$
• $P_2$:
  $64\cdot t^{49}-784\cdot t^{47}+4508\cdot t^{45}-16170\cdot t^{43}+\frac{162239}{4}\cdot t^{41}-\frac{604709}{8}\cdot t^{39}+\frac{3473561}{32}\cdot t^{37}-\frac{7868679}{64}\cdot t^{35}+\frac{114191805}{1024}\cdot t^{33}-\frac{83740657}{1024}\cdot t^{31}+\frac{199689259}{4096}\cdot t^{29}-\frac{193956553}{8192}\cdot t^{27}+\frac{613322073}{65536}\cdot t^{25}-\frac{393155175}{131072}\cdot t^{23}+\frac{405992895}{524288}\cdot t^{21}-\frac{167173545}{1048576}\cdot t^{19}+\frac{866262915}{33554432}\cdot t^{17}-\frac{866262915}{268435456}\cdot t^{15}+\frac{326012925}{1073741824}\cdot t^{13}-\frac{44612295}{2147483648}\cdot t^{11}+\frac{16921905}{17179869184}\cdot t^9-\frac{1036035}{34359738368}\cdot t^7+\frac{73255}{137438953472}\cdot t^5-\frac{1225}{274877906944}\cdot t^3+\frac{49}{4398046511104}\cdot t$
• $P_3$:
  $64\cdot t^{99}-1600\cdot t^{97}+19396\cdot t^{95}-151904\cdot t^{93}+\frac{3455911}{4}\cdot t^{91}-\frac{15214017}{4}\cdot t^{89}+\frac{431636205}{32}\cdot t^{87}-\frac{633601947}{16}\cdot t^{85}+\frac{100510755103}{1024}\cdot t^{83}-\frac{213462842923}{1024}\cdot t^{81}+\frac{3143076243093}{8192}\cdot t^{79}-\frac{1264605215445}{2048}\cdot t^{77}+\frac{114712258885497}{131072}\cdot t^{75}-\frac{144009382295835}{131072}\cdot t^{73}+\frac{1287001465389855}{1048576}\cdot t^{71}-\frac{642075792533955}{524288}\cdot t^{69}+\frac{73463333211193725}{67108864}\cdot t^{67}-\frac{58966534364198285}{67108864}\cdot t^{65}+\frac{170312526436271505}{268435456}\cdot t^{63}-\frac{6923541417747955}{16777216}\cdot t^{61}+\frac{1039381224624331435}{4294967296}\cdot t^{59}-\frac{549787618016776325}{4294967296}\cdot t^{57}+\frac{2098754472255346145}{34359738368}\cdot t^{55}-\frac{451594925861341491}{17179869184}\cdot t^{53}+\frac{11210250708811416249}{1099511627776}\cdot t^{51}-\frac{3915098242983841797}{1099511627776}\cdot t^{49}+\frac{9835900646046041175}{8796093022208}\cdot t^{47}-\frac{693166728542340241}{2199023255552}\cdot t^{45}+\frac{11201515214546688031}{140737488355328}\cdot t^{43}-\frac{2526954273598394101}{140737488355328}\cdot t^{41}+\frac{4062103501709746801}{1125899906842624}\cdot t^{39}-\frac{362228495317153465}{562949953421312}\cdot t^{37}+\frac{14617825892237136387}{144115188075855872}\cdot t^{35}-\frac{2026993368012259227}{144115188075855872}\cdot t^{33}+\frac{7867870309198269699}{4611686018427387904}\cdot t^{31}-\frac{103679143530959731}{576460752303423488}\cdot t^{29}+\frac{1206738118441740605}{73786976294838206464}\cdot t^{27}-\frac{93814158561717867}{73786976294838206464}\cdot t^{25}+\frac{49365616202473935}{590295810358705651712}\cdot t^{23}-\frac{1356682523670705}{295147905179352825856}\cdot t^{21}+\frac{3928884456931665}{18889465931478580854784}\cdot t^{19}-\frac{143709797956725}{18889465931478580854784}\cdot t^{17}+\frac{33232090492755}{151115727451828646838272}\cdot t^{15}-\frac{184389213015}{37778931862957161709568}\cdot t^{13}+\frac{193661512135}{2417851639229258349412352}\cdot t^{11}-\frac{2232529845}{2417851639229258349412352}\cdot t^9+\frac{134371825}{19342813113834066795298816}\cdot t^7-\frac{294245}{9671406556917033397649408}\cdot t^5+\frac{78449}{1237940039285380274899124224}\cdot t^3-\frac{49}{1237940039285380274899124224}\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.