Rule: Q[4, 88]

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^{92}-184\cdot t^{90}+2047\cdot t^{88}-14674\cdot t^{86}+\frac{2437885}{32}\cdot t^{84}-\frac{9768353}{32}\cdot t^{82}+\frac{251478297}{256}\cdot t^{80}-\frac{166947777}{64}\cdot t^{78}+\frac{23873532111}{4096}\cdot t^{76}-\frac{45541878525}{4096}\cdot t^{74}+\frac{600042019005}{32768}\cdot t^{72}-\frac{430333165145}{16384}\cdot t^{70}+\frac{69283639588345}{2097152}\cdot t^{68}-\frac{76839401646665}{2097152}\cdot t^{66}+\frac{603738155795225}{16777216}\cdot t^{64}-\frac{32931172134285}{1048576}\cdot t^{62}+\frac{3277518237154365}{134217728}\cdot t^{60}-\frac{2274983246965971}{134217728}\cdot t^{58}+\frac{11292934856560811}{1073741824}\cdot t^{56}-\frac{3134664686211905}{536870912}\cdot t^{54}+\frac{99682337021538579}{34359738368}\cdot t^{52}-\frac{44325546240965847}{34359738368}\cdot t^{50}+\frac{141035828948527695}{274877906944}\cdot t^{48}-\frac{12530593498262385}{68719476736}\cdot t^{46}+\frac{254297338641207225}{4398046511104}\cdot t^{44}-\frac{71810532046143891}{4398046511104}\cdot t^{42}+\frac{144123235645058019}{35184372088832}\cdot t^{40}-\frac{16013692849450891}{17592186044416}\cdot t^{38}+\frac{1608232296166282339}{9007199254740992}\cdot t^{36}-\frac{277281430373496955}{9007199254740992}\cdot t^{34}+\frac{334526628902218907}{72057594037927936}\cdot t^{32}-\frac{5484043096757687}{9007199254740992}\cdot t^{30}+\frac{159037249805972923}{2305843009213693952}\cdot t^{28}-\frac{15438130566681501}{2305843009213693952}\cdot t^{26}+\frac{10177266600753525}{18446744073709551616}\cdot t^{24}-\frac{351995686943355}{9223372036854775808}\cdot t^{22}+\frac{1290650852125635}{590295810358705651712}\cdot t^{20}-\frac{60251513981295}{590295810358705651712}\cdot t^{18}+\frac{17969749783895}{4722366482869645213696}\cdot t^{16}-\frac{130404570275}{1180591620717411303424}\cdot t^{14}+\frac{182566398385}{75557863725914323419136}\cdot t^{12}-\frac{2881248755}{75557863725914323419136}\cdot t^{10}+\frac{246964179}{604462909807314587353088}\cdot t^8-\frac{820479}{302231454903657293676544}\cdot t^6+\frac{372945}{38685626227668133590597632}\cdot t^4-\frac{529}{38685626227668133590597632}\cdot t^2+\frac{1}{309485009821345068724781056}$

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.