Rule: Q[4, 72]

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.

• $P_1$:
  $8\cdot t^4-8\cdot t^2+1$
• $P_2$:
  $8\cdot t^{76}-152\cdot t^{74}+1387\cdot t^{72}-8094\cdot t^{70}+\frac{1085945}{32}\cdot t^{68}-\frac{3484201}{32}\cdot t^{66}+\frac{71177249}{256}\cdot t^{64}-\frac{9283989}{16}\cdot t^{62}+\frac{1032707247}{1024}\cdot t^{60}-\frac{1515664865}{1024}\cdot t^{58}+\frac{15184206193}{8192}\cdot t^{56}-\frac{8176111027}{4096}\cdot t^{54}+\frac{3900004959879}{2097152}\cdot t^{52}-\frac{3157146872283}{2097152}\cdot t^{50}+\frac{17822603311275}{16777216}\cdot t^{48}-\frac{2746433952885}{4194304}\cdot t^{46}+\frac{189503942749065}{536870912}\cdot t^{44}-\frac{89367263130915}{536870912}\cdot t^{42}+\frac{294809247339915}{4294967296}\cdot t^{40}-\frac{53081997443475}{2147483648}\cdot t^{38}+\frac{1066189834364655}{137438953472}\cdot t^{36}-\frac{290779045735815}{137438953472}\cdot t^{34}+\frac{549249308612095}{1099511627776}\cdot t^{32}-\frac{13967783894155}{137438953472}\cdot t^{30}+\frac{155794512665575}{8796093022208}\cdot t^{28}-\frac{23094245406897}{8796093022208}\cdot t^{26}+\frac{23094245406897}{70368744177664}\cdot t^{24}-\frac{1204461778591}{35184372088832}\cdot t^{22}+\frac{13249079564501}{4503599627370496}\cdot t^{20}-\frac{923450153065}{4503599627370496}\cdot t^{18}+\frac{409530067881}{36028797018963968}\cdot t^{16}-\frac{4403549117}{9007199254740992}\cdot t^{14}+\frac{36429360877}{2305843009213693952}\cdot t^{12}-\frac{847194439}{2305843009213693952}\cdot t^{10}+\frac{106789215}{18446744073709551616}\cdot t^8-\frac{520923}{9223372036854775808}\cdot t^6+\frac{173641}{590295810358705651712}\cdot t^4-\frac{361}{590295810358705651712}\cdot t^2+\frac{1}{4722366482869645213696}$

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.