Rule: Q[2, 90]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^{92}-91\cdot t^{90}+\frac{4005}{4}\cdot t^{88}-\frac{28391}{4}\cdot t^{86}+\frac{1165945}{32}\cdot t^{84}-\frac{36949857}{256}\cdot t^{82}+\frac{470155077}{1024}\cdot t^{80}-\frac{616980915}{512}\cdot t^{78}+\frac{21797572797}{8192}\cdot t^{76}-\frac{164346779025}{32768}\cdot t^{74}+\frac{1069640120835}{131072}\cdot t^{72}-\frac{1515521146815}{131072}\cdot t^{70}+\frac{15061660780075}{1048576}\cdot t^{68}-\frac{263926640438545}{16777216}\cdot t^{66}+\frac{1023729916348425}{67108864}\cdot t^{64}-\frac{110247837145215}{8388608}\cdot t^{62}+\frac{2707515065475345}{268435456}\cdot t^{60}-\frac{7418423631410775}{1073741824}\cdot t^{58}+\frac{18166895204032609}{4294967296}\cdot t^{56}-\frac{9949153134498655}{4294967296}\cdot t^{54}+\frac{39006131877993357}{34359738368}\cdot t^{52}-\frac{136831034048198919}{274877906944}\cdot t^{50}+\frac{214619739704281275}{1099511627776}\cdot t^{48}-\frac{37591780494787155}{549755813888}\cdot t^{46}+\frac{187958902473935775}{8796093022208}\cdot t^{44}-\frac{209187202047462639}{35184372088832}\cdot t^{42}+\frac{206785512012474549}{140737488355328}\cdot t^{40}-\frac{45256088487578605}{140737488355328}\cdot t^{38}+\frac{69923143311577493}{1125899906842624}\cdot t^{36}-\frac{759510004936100355}{72057594037927936}\cdot t^{34}+\frac{450883717216034179}{288230376151711744}\cdot t^{32}-\frac{14544636039226909}{72057594037927936}\cdot t^{30}+\frac{103719945525634515}{4611686018427387904}\cdot t^{28}-\frac{39602161018878633}{18446744073709551616}\cdot t^{26}+\frac{12832205713993575}{73786976294838206464}\cdot t^{24}-\frac{872337137207445}{73786976294838206464}\cdot t^{22}+\frac{392806781081715}{590295810358705651712}\cdot t^{20}-\frac{144079707346575}{4722366482869645213696}\cdot t^{18}+\frac{21094923659355}{18889465931478580854784}\cdot t^{16}-\frac{300497488025}{9444732965739290427392}\cdot t^{14}+\frac{103189703435}{151115727451828646838272}\cdot t^{12}-\frac{6388855935}{604462909807314587353088}\cdot t^{10}+\frac{268439325}{2417851639229258349412352}\cdot t^8-\frac{1747977}{2417851639229258349412352}\cdot t^6+\frac{48645}{19342813113834066795298816}\cdot t^4-\frac{1081}{309485009821345068724781056}\cdot t^2+\frac{1}{1237940039285380274899124224}$

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.