Rule: Q[4, 80]

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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{84}-332\cdot t^{82}+3321\cdot t^{80}-21330\cdot t^{78}+\frac{395395}{4}\cdot t^{76}-\frac{22537515}{64}\cdot t^{74}+\frac{256851595}{256}\cdot t^{72}-\frac{601202085}{256}\cdot t^{70}+\frac{18855883575}{4096}\cdot t^{68}-\frac{125595622175}{16384}\cdot t^{66}+\frac{718406958841}{65536}\cdot t^{64}-\frac{111203042769}{8192}\cdot t^{62}+\frac{960205268841}{65536}\cdot t^{60}-\frac{7263091136105}{524288}\cdot t^{58}+\frac{24156719613645}{2097152}\cdot t^{56}-\frac{17714927716673}{2097152}\cdot t^{54}+\frac{367392196558827}{67108864}\cdot t^{52}-\frac{842840921517309}{268435456}\cdot t^{50}+\frac{1712239019666175}{1073741824}\cdot t^{48}-\frac{385048966145025}{536870912}\cdot t^{46}+\frac{1226232861415695}{4294967296}\cdot t^{44}-\frac{27619435402363035}{274877906944}\cdot t^{42}+\frac{34315056105966195}{1099511627776}\cdot t^{40}-\frac{9384903142585425}{1099511627776}\cdot t^{38}+\frac{36052387482172425}{17592186044416}\cdot t^{36}-\frac{30284005485024837}{70368744177664}\cdot t^{34}+\frac{22150361247847371}{281474976710656}\cdot t^{32}-\frac{876961939569947}{70368744177664}\cdot t^{30}+\frac{956086325095055}{562949953421312}\cdot t^{28}-\frac{890149337157465}{4503599627370496}\cdot t^{26}+\frac{350664890395365}{18014398509481984}\cdot t^{24}-\frac{28907858348005}{18014398509481984}\cdot t^{22}+\frac{125994627894135}{1152921504606846976}\cdot t^{20}-\frac{27900908274925}{4611686018427387904}\cdot t^{18}+\frac{4923689695575}{18446744073709551616}\cdot t^{16}-\frac{84406109067}{9223372036854775808}\cdot t^{14}+\frac{17417133617}{73786976294838206464}\cdot t^{12}-\frac{5178066751}{1180591620717411303424}\cdot t^{10}+\frac{260932815}{4722366482869645213696}\cdot t^8-\frac{2036265}{4722366482869645213696}\cdot t^6+\frac{135751}{75557863725914323419136}\cdot t^4-\frac{903}{302231454903657293676544}\cdot t^2+\frac{1}{1208925819614629174706176}$

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.