Rule: Q[22, 46]

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.

• $P_1$:
  $4194304\cdot t^{22}-22020096\cdot t^{20}+49807360\cdot t^{18}-63504384\cdot t^{16}+50135040\cdot t^{14}-25346048\cdot t^{12}+8200192\cdot t^{10}-1647360\cdot t^8+192192\cdot t^6-11440\cdot t^4+264\cdot t^2-1$
• $P_2$:
  $4194304\cdot t^{68}-70254592\cdot t^{66}+562298880\cdot t^{64}-2862612480\cdot t^{62}+10410000384\cdot t^{60}-28790157312\cdot t^{58}+62949907456\cdot t^{56}-111685319680\cdot t^{54}+163751734080\cdot t^{52}-201050740176\cdot t^{50}+208717929420\cdot t^{48}-184509266760\cdot t^{46}+139595826825\cdot t^{44}-\frac{725591495475}{8}\cdot t^{42}+\frac{1622686435335}{32}\cdot t^{40}-\frac{781293468865}{32}\cdot t^{38}+\frac{10363194502115}{1024}\cdot t^{36}-\frac{14771069086725}{4096}\cdot t^{34}+\frac{18053528883775}{16384}\cdot t^{32}-\frac{1178230306099}{4096}\cdot t^{30}+\frac{2091959931237}{32768}\cdot t^{28}-\frac{6275879793711}{524288}\cdot t^{26}+\frac{3945185556975}{2097152}\cdot t^{24}-\frac{514589420475}{2097152}\cdot t^{22}+\frac{880519675035}{33554432}\cdot t^{20}-\frac{304179524103}{134217728}\cdot t^{18}+\frac{83254860801}{536870912}\cdot t^{16}-\frac{2202509545}{268435456}\cdot t^{14}+\frac{698356685}{2147483648}\cdot t^{12}-\frac{158936349}{17179869184}\cdot t^{10}+\frac{12225873}{68719476736}\cdot t^8-\frac{145299}{68719476736}\cdot t^6+\frac{58905}{4398046511104}\cdot t^4-\frac{595}{17592186044416}\cdot t^2+\frac{1}{70368744177664}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.