Rule: Q[10, 66]

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.

• $P_1$:
  $1024\cdot t^{10}-2304\cdot t^8+1792\cdot t^6-560\cdot t^4+60\cdot t^2-1$
• $P_2$:
  $1024\cdot t^{76}-19200\cdot t^{74}+172864\cdot t^{72}-995136\cdot t^{70}+4115160\cdot t^{68}-13019909\cdot t^{66}+\frac{131115985}{4}\cdot t^{64}-67431078\cdot t^{62}+\frac{924001221}{8}\cdot t^{60}-\frac{5344712945}{32}\cdot t^{58}+\frac{26372568651}{128}\cdot t^{56}-\frac{27970906145}{128}\cdot t^{54}+\frac{205263418941}{1024}\cdot t^{52}-\frac{10468434365991}{65536}\cdot t^{50}+\frac{29078984349975}{262144}\cdot t^{48}-\frac{8817498480315}{131072}\cdot t^{46}+\frac{149608375854525}{4194304}\cdot t^{44}-\frac{277508869722315}{16777216}\cdot t^{42}+\frac{449972009097765}{67108864}\cdot t^{40}-\frac{159245992330425}{67108864}\cdot t^{38}+\frac{392806781081715}{536870912}\cdot t^{36}-\frac{841728816603675}{4294967296}\cdot t^{34}+\frac{780512175396135}{17179869184}\cdot t^{32}-\frac{38962765599485}{4294967296}\cdot t^{30}+\frac{106596245508025}{68719476736}\cdot t^{28}-\frac{61989816618513}{274877906944}\cdot t^{26}+\frac{30387165009075}{1099511627776}\cdot t^{24}-\frac{3106243534261}{1099511627776}\cdot t^{22}+\frac{2091959931237}{8796093022208}\cdot t^{20}-\frac{2284324062845}{140737488355328}\cdot t^{18}+\frac{495746924277}{562949953421312}\cdot t^{16}-\frac{10429458435}{281474976710656}\cdot t^{14}+\frac{21090682613}{18014398509481984}\cdot t^{12}-\frac{1917334783}{72057594037927936}\cdot t^{10}+\frac{118030185}{288230376151711744}\cdot t^8-\frac{1124097}{288230376151711744}\cdot t^6+\frac{45695}{2305843009213693952}\cdot t^4-\frac{741}{18446744073709551616}\cdot t^2+\frac{1}{73786976294838206464}$

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.