Rule: Q[4, 35, 40, 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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{39}-152\cdot t^{37}+666\cdot t^{35}-1785\cdot t^{33}+\frac{6545}{2}\cdot t^{31}-\frac{17391}{4}\cdot t^{29}+\frac{69223}{16}\cdot t^{27}-\frac{105183}{32}\cdot t^{25}+\frac{7888725}{4096}\cdot t^{23}-\frac{7153575}{8192}\cdot t^{21}+\frac{10015005}{32768}\cdot t^{19}-\frac{5368545}{65536}\cdot t^{17}+\frac{4345965}{262144}\cdot t^{15}-\frac{1300075}{524288}\cdot t^{13}+\frac{557175}{2097152}\cdot t^{11}-\frac{81719}{4194304}\cdot t^9+\frac{245157}{268435456}\cdot t^7-\frac{13167}{536870912}\cdot t^5+\frac{665}{2147483648}\cdot t^3-\frac{5}{4294967296}\cdot t$
• $P_3$:
  $16\cdot t^{79}-312\cdot t^{77}+2926\cdot t^{75}-17575\cdot t^{73}+\frac{607725}{8}\cdot t^{71}-\frac{4027191}{16}\cdot t^{69}+\frac{42557613}{64}\cdot t^{67}-\frac{184138713}{128}\cdot t^{65}+\frac{1329890705}{512}\cdot t^{63}-\frac{4064595535}{1024}\cdot t^{61}+\frac{21252028083}{4096}\cdot t^{59}-\frac{47908063307}{8192}\cdot t^{57}+\frac{374810142343}{65536}\cdot t^{55}-\frac{639027625005}{131072}\cdot t^{53}+\frac{1906017461595}{524288}\cdot t^{51}-\frac{2492484372855}{1048576}\cdot t^{49}+\frac{366395202809685}{268435456}\cdot t^{47}-\frac{369816259792035}{536870912}\cdot t^{45}+\frac{656125622211675}{2147483648}\cdot t^{43}-\frac{511200549488475}{4294967296}\cdot t^{41}+\frac{1397281501935165}{34359738368}\cdot t^{39}-\frac{835662302610135}{68719476736}\cdot t^{37}+\frac{872337137207445}{274877906944}\cdot t^{35}-\frac{395911973027025}{549755813888}\cdot t^{33}+\frac{622147386185325}{4398046511104}\cdot t^{31}-\frac{210398934237219}{8796093022208}\cdot t^{29}+\frac{121683714103007}{35184372088832}\cdot t^{27}-\frac{29846948742247}{70368744177664}\cdot t^{25}+\frac{24599133578775}{562949953421312}\cdot t^{23}-\frac{4207965378925}{1125899906842624}\cdot t^{21}+\frac{1178230306099}{4503599627370496}\cdot t^{19}-\frac{132638171391}{9007199254740992}\cdot t^{17}+\frac{751616304549}{1152921504606846976}\cdot t^{15}-\frac{50883115395}{2305843009213693952}\cdot t^{13}+\frac{5075297955}{9223372036854775808}\cdot t^{11}-\frac{177232627}{18446744073709551616}\cdot t^9+\frac{16112057}{147573952589676412928}\cdot t^7-\frac{212667}{295147905179352825856}\cdot t^5+\frac{2665}{1180591620717411303424}\cdot t^3-\frac{5}{2361183241434822606848}\cdot t$
• $P_4$:
  $16\cdot t^{159}-632\cdot t^{157}+12246\cdot t^{155}-155155\cdot t^{153}+\frac{11565015}{8}\cdot t^{151}-\frac{168998445}{16}\cdot t^{149}+\frac{4033283235}{64}\cdot t^{147}-\frac{40411916335}{128}\cdot t^{145}+\frac{2775660569325}{2048}\cdot t^{143}-\frac{20736778337275}{4096}\cdot t^{141}+\frac{272896002918539}{16384}\cdot t^{139}-\frac{1596916146425691}{32768}\cdot t^{137}+\frac{33506465811039949}{262144}\cdot t^{135}-\frac{158590258116617655}{524288}\cdot t^{133}+\frac{1362138244371496845}{2097152}\cdot t^{131}-\frac{5332692942907262361}{4194304}\cdot t^{129}+\frac{76435265515004093841}{33554432}\cdot t^{127}-\frac{251566663671553992111}{67108864}\cdot t^{125}+\frac{1525541192061458089875}{268435456}\cdot t^{123}-\frac{4272540337453198972875}{536870912}\cdot t^{121}+\frac{44312346928443177918675}{4294967296}\cdot t^{119}-\frac{106583414794312967511825}{8589934592}\cdot t^{117}+\frac{476465779179320024726775}{34359738368}\cdot t^{115}-\frac{991187934789096401803875}{68719476736}\cdot t^{113}+\frac{15373130518003436349546375}{1099511627776}\cdot t^{111}-\frac{27808284981455104863401665}{2199023255552}\cdot t^{109}+\frac{93960714925858063849587945}{8796093022208}\cdot t^{107}-\frac{148385189179766382648569545}{17592186044416}\cdot t^{105}+\frac{876821572425892261105183675}{140737488355328}\cdot t^{103}-\frac{1212409507752885508709010225}{281474976710656}\cdot t^{101}+\frac{3139829750847216317425898275}{1125899906842624}\cdot t^{99}-\frac{3808780725521341924439367975}{2251799813685248}\cdot t^{97}+\frac{1108355191126710500011856080725}{1152921504606846976}\cdot t^{95}-\frac{1180817448909750031627997470875}{2305843009213693952}\cdot t^{93}+\frac{2358327285917792079974123800375}{9223372036854775808}\cdot t^{91}-\frac{2207394339619053386855779877151}{18446744073709551616}\cdot t^{89}+\frac{7745659707838900594020818995451}{147573952589676412928}\cdot t^{87}-\frac{6367065033404818088822650815641}{295147905179352825856}\cdot t^{85}+\frac{9806049253345643044476645130215}{1180591620717411303424}\cdot t^{83}-\frac{7071410385491676897722827585955}{2361183241434822606848}\cdot t^{81}+\frac{38185616081655055247703268964157}{37778931862957161709568}\cdot t^{79}-\frac{24113523908091663295383023504523}{75557863725914323419136}\cdot t^{77}+\frac{28473031055317274738616112499691}{302231454903657293676544}\cdot t^{75}-\frac{15705160242199450884448362589275}{604462909807314587353088}\cdot t^{73}+\frac{32345737552116110442265122950325}{4835703278458516698824704}\cdot t^{71}-\frac{15532204409083774772759194305615}{9671406556917033397649408}\cdot t^{69}+\frac{13897235523917061638784542273445}{38685626227668133590597632}\cdot t^{67}-\frac{5785499480960388492440712288945}{77371252455336267181195264}\cdot t^{65}+\frac{17907498393448821524221252322925}{1237940039285380274899124224}\cdot t^{63}-\frac{6430105600736449427616125351475}{2475880078570760549798248448}\cdot t^{61}+\frac{4278942999762800891831821597527}{9903520314283042199192993792}\cdot t^{59}-\frac{1317012317430140731412888424783}{19807040628566084398385987584}\cdot t^{57}+\frac{1497116565967595874170206499967}{158456325028528675187087900672}\cdot t^{55}-\frac{392032816163265715595619229845}{316912650057057350374175801344}\cdot t^{53}+\frac{188756541115646455657149999555}{1267650600228229401496703205376}\cdot t^{51}-\frac{41673522064493373326903246655}{2535301200456458802993406410752}\cdot t^{49}+\frac{67318766411873910758843706135}{40564819207303340847894502572032}\cdot t^{47}-\frac{12395092231516896189799019985}{81129638414606681695789005144064}\cdot t^{45}+\frac{4148458860446831381981416425}{324518553658426726783156020576256}\cdot t^{43}-\frac{628638756667811501582349225}{649037107316853453566312041152512}\cdot t^{41}+\frac{343655853645070287531684243}{5192296858534827628530496329220096}\cdot t^{39}-\frac{42167409761715032796982617}{10384593717069655257060992658440192}\cdot t^{37}+\frac{9244073371067219171425419}{41538374868278621028243970633760768}\cdot t^{35}-\frac{900052962818686860906255}{83076749736557242056487941267521536}\cdot t^{33}+\frac{9900582591005555469968805}{21267647932558653966460912964485513216}\cdot t^{31}-\frac{745549944100013488831659}{42535295865117307932921825928971026432}\cdot t^{29}+\frac{97580037815798025939927}{170141183460469231731687303715884105728}\cdot t^{27}-\frac{5496805211578415519967}{340282366920938463463374607431768211456}\cdot t^{25}+\frac{1054374401197905790275}{2722258935367507707706996859454145691648}\cdot t^{23}-\frac{42483950231417449425}{5444517870735015415413993718908291383296}\cdot t^{21}+\frac{2832263348761163295}{21778071482940061661655974875633165533184}\cdot t^{19}-\frac{76644569178376155}{43556142965880123323311949751266331066368}\cdot t^{17}+\frac{13161188646791865}{696898287454081973172991196020261297061888}\cdot t^{15}-\frac{217591687594575}{1393796574908163946345982392040522594123776}\cdot t^{13}+\frac{5333800010175}{5575186299632655785383929568162090376495104}\cdot t^{11}-\frac{46017098127}{11150372599265311570767859136324180752990208}\cdot t^9+\frac{1037979657}{89202980794122492566142873090593446023921664}\cdot t^7-\frac{3410667}{178405961588244985132285746181186892047843328}\cdot t^5+\frac{10665}{713623846352979940529142984724747568191373312}\cdot t^3-\frac{5}{1427247692705959881058285969449495136382746624}\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.