Rule: Q[6, 42, 49]

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.

• $P_1$:
  $64\cdot t^6-80\cdot t^4+24\cdot t^2-1$
• $P_2$:
  $64\cdot t^{48}-752\cdot t^{46}+4140\cdot t^{44}-14190\cdot t^{42}+\frac{135751}{4}\cdot t^{40}-\frac{481299}{8}\cdot t^{38}+\frac{2622893}{32}\cdot t^{36}-\frac{5620485}{64}\cdot t^{34}+\frac{76904685}{1024}\cdot t^{32}-\frac{52978783}{1024}\cdot t^{30}+\frac{118183439}{4096}\cdot t^{28}-\frac{106874019}{8192}\cdot t^{26}+\frac{312919425}{65536}\cdot t^{24}-\frac{184542225}{131072}\cdot t^{22}+\frac{173996955}{524288}\cdot t^{20}-\frac{64822395}{1048576}\cdot t^{18}+\frac{300540195}{33554432}\cdot t^{16}-\frac{265182525}{268435456}\cdot t^{14}+\frac{86493225}{1073741824}\cdot t^{12}-\frac{10015005}{2147483648}\cdot t^{10}+\frac{3108105}{17179869184}\cdot t^8-\frac{148005}{34359738368}\cdot t^6+\frac{7475}{137438953472}\cdot t^4-\frac{75}{274877906944}\cdot t^2+\frac{1}{4398046511104}$
• $P_3$:
  $64\cdot t^{97}-1536\cdot t^{95}+17860\cdot t^{93}-134044\cdot t^{91}+\frac{2919735}{4}\cdot t^{89}-\frac{6147141}{2}\cdot t^{87}+\frac{333281949}{32}\cdot t^{85}-\frac{933921945}{32}\cdot t^{83}+\frac{70625252863}{1024}\cdot t^{81}-\frac{35709397515}{256}\cdot t^{79}+\frac{2000375522613}{8192}\cdot t^{77}-\frac{3058045339167}{8192}\cdot t^{75}+\frac{65783533458825}{131072}\cdot t^{73}-\frac{39112924418505}{65536}\cdot t^{71}+\frac{661194674693775}{1048576}\cdot t^{69}-\frac{622956910374135}{1048576}\cdot t^{67}+\frac{33594090947249085}{67108864}\cdot t^{65}-\frac{1585777713559325}{4194304}\cdot t^{63}+\frac{68822752768474705}{268435456}\cdot t^{61}-\frac{41953909915492575}{268435456}\cdot t^{59}+\frac{368118665976450235}{4294967296}\cdot t^{57}-\frac{90834476020163045}{2147483648}\cdot t^{55}+\frac{645402855932737425}{34359738368}\cdot t^{53}-\frac{257786995789945557}{34359738368}\cdot t^{51}+\frac{2961066843533158425}{1099511627776}\cdot t^{49}-\frac{238507849862670843}{274877906944}\cdot t^{47}+\frac{2203649450440574199}{8796093022208}\cdot t^{45}-\frac{569017463728786765}{8796093022208}\cdot t^{43}+\frac{2097235794886099791}{140737488355328}\cdot t^{41}-\frac{214859239356147155}{70368744177664}\cdot t^{39}+\frac{624355672011392321}{1125899906842624}\cdot t^{37}-\frac{100101318622914609}{1125899906842624}\cdot t^{35}+\frac{1804857108504066435}{144115188075855872}\cdot t^{33}-\frac{27767032438524099}{18014398509481984}\cdot t^{31}+\frac{759510004936100355}{4611686018427387904}\cdot t^{29}-\frac{69923143311577493}{4611686018427387904}\cdot t^{27}+\frac{87967825456500717}{73786976294838206464}\cdot t^{25}-\frac{2923166552608575}{36893488147419103232}\cdot t^{23}+\frac{2594951360736735}{590295810358705651712}\cdot t^{21}-\frac{118413686604675}{590295810358705651712}\cdot t^{19}+\frac{139646485582065}{18889465931478580854784}\cdot t^{17}-\frac{1015828093665}{4722366482869645213696}\cdot t^{15}+\frac{725591495475}{151115727451828646838272}\cdot t^{13}-\frac{11965356585}{151115727451828646838272}\cdot t^{11}+\frac{2215806775}{2417851639229258349412352}\cdot t^9-\frac{8361535}{1208925819614629174706176}\cdot t^7+\frac{587265}{19342813113834066795298816}\cdot t^5-\frac{1225}{19342813113834066795298816}\cdot t^3+\frac{49}{1237940039285380274899124224}\cdot t$

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.