Rule: Q[8, 64]

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.

• $P_1$:
  $128\cdot t^8-256\cdot t^6+160\cdot t^4-32\cdot t^2+1$
• $P_2$:
  $128\cdot t^{72}-2304\cdot t^{70}+19872\cdot t^{68}-109344\cdot t^{66}+431145\cdot t^{64}-1297296\cdot t^{62}+3097458\cdot t^{60}-6024726\cdot t^{58}+\frac{4979436039}{512}\cdot t^{56}-\frac{3381098545}{256}\cdot t^{54}+\frac{31215174309}{2048}\cdot t^{52}-\frac{30843011277}{2048}\cdot t^{50}+\frac{839615306985}{65536}\cdot t^{48}-\frac{154349098155}{16384}\cdot t^{46}+\frac{786952298475}{131072}\cdot t^{44}-\frac{435354897285}{131072}\cdot t^{42}+\frac{53548652366055}{33554432}\cdot t^{40}-\frac{11167900760835}{16777216}\cdot t^{38}+\frac{32308782859535}{134217728}\cdot t^{36}-\frac{10106520954075}{134217728}\cdot t^{34}+\frac{87227050080555}{4294967296}\cdot t^{32}-\frac{2524779227355}{536870912}\cdot t^{30}+\frac{3993741686907}{4294967296}\cdot t^{28}-\frac{669757922649}{4294967296}\cdot t^{26}+\frac{24185702762325}{1099511627776}\cdot t^{24}-\frac{1420266800511}{549755813888}\cdot t^{22}+\frac{1097262979659}{4398046511104}\cdot t^{20}-\frac{85794224747}{4398046511104}\cdot t^{18}+\frac{170474238783}{140737488355328}\cdot t^{16}-\frac{2050612335}{35184372088832}\cdot t^{14}+\frac{592399119}{281474976710656}\cdot t^{12}-\frac{15380937}{281474976710656}\cdot t^{10}+\frac{138428433}{144115188075855872}\cdot t^8-\frac{752913}{72057594037927936}\cdot t^6+\frac{34965}{576460752303423488}\cdot t^4-\frac{81}{576460752303423488}\cdot t^2+\frac{1}{18446744073709551616}$

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.