Rule: Q[2, 90, 93]

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}$
• $P_3$:
  $4\cdot t^{185}-184\cdot t^{183}+\frac{16653}{4}\cdot t^{181}-\frac{247065}{4}\cdot t^{179}+\frac{43252665}{64}\cdot t^{177}-\frac{93052971}{16}\cdot t^{175}+\frac{10494307285}{256}\cdot t^{173}-\frac{62304191455}{256}\cdot t^{171}+\frac{10175184525825}{8192}\cdot t^{169}-\frac{22669008086725}{4096}\cdot t^{167}+\frac{5713002201638095}{262144}\cdot t^{165}-\frac{20077122022899591}{262144}\cdot t^{163}+\frac{1015625448537713793}{4194304}\cdot t^{161}-\frac{363529784825637885}{524288}\cdot t^{159}+\frac{15170424010614077985}{8388608}\cdot t^{157}-\frac{36213842579723196687}{8388608}\cdot t^{155}+\frac{5084849543399957087757}{536870912}\cdot t^{153}-\frac{5145025277641376698263}{268435456}\cdot t^{151}+\frac{308293181318987254538775}{8589934592}\cdot t^{149}-\frac{535650900917610064378275}{8589934592}\cdot t^{147}+\frac{13850770645173189399622335}{137438953472}\cdot t^{145}-\frac{5216524009221071332325295}{34359738368}\cdot t^{143}+\frac{117435406353928020481371885}{549755813888}\cdot t^{141}-\frac{154586217753170120318903775}{549755813888}\cdot t^{139}+\frac{6101384421689936724191794675}{17592186044416}\cdot t^{137}-\frac{3530465669097108728109985043}{8796093022208}\cdot t^{135}+\frac{491277876568974591473150995599}{1125899906842624}\cdot t^{133}-\frac{502263824891970529227966391727}{1125899906842624}\cdot t^{131}+\frac{7733772999918859053121399322885}{18014398509481984}\cdot t^{129}-\frac{219120737313756384329598179805}{562949953421312}\cdot t^{127}+\frac{2996897468798914241061735105333}{9007199254740992}\cdot t^{125}-\frac{2416852797418479226662689601075}{9007199254740992}\cdot t^{123}+\frac{235501903104296748540911169829425}{1152921504606846976}\cdot t^{121}-\frac{84657546867557654704249113337375}{576460752303423488}\cdot t^{119}+\frac{1840187729279016389097625463596625}{18446744073709551616}\cdot t^{117}-\frac{1181410967917446094268352544556925}{18446744073709551616}\cdot t^{115}+\frac{11472813177331643182117112488252805}{295147905179352825856}\cdot t^{113}-\frac{1646108329996250636142687462036635}{73786976294838206464}\cdot t^{111}+\frac{14295151286809544998081233222949725}{1180591620717411303424}\cdot t^{109}-\frac{7338327269680881027272469802047975}{1180591620717411303424}\cdot t^{107}+\frac{114015490264000757001814181499764565}{37778931862957161709568}\cdot t^{105}-\frac{26178493559354252869213853279592705}{18889465931478580854784}\cdot t^{103}+\frac{727595908292528520222118366548679785}{1208925819614629174706176}\cdot t^{101}-\frac{298776982995386975696999329246286625}{1208925819614629174706176}\cdot t^{99}+\frac{1855783795788248680033474707008625375}{19342813113834066795298816}\cdot t^{97}-\frac{85111597253645447736759832898267925}{2417851639229258349412352}\cdot t^{95}+\frac{472078610854070713223146153901573025}{38685626227668133590597632}\cdot t^{93}-\frac{154565459760731249898103416989968575}{38685626227668133590597632}\cdot t^{91}+\frac{3057708008310118204505958901323291375}{2475880078570760549798248448}\cdot t^{89}-\frac{445925240598183483123988345657009125}{1237940039285380274899124224}\cdot t^{87}+\frac{3925191353124245671451389179065579145}{39614081257132168796771975168}\cdot t^{85}-\frac{1017642202661841470376286083461446445}{39614081257132168796771975168}\cdot t^{83}+\frac{3975931590882028155787028176830427385}{633825300114114700748351602688}\cdot t^{81}-\frac{228436983161756476534791660039200325}{158456325028528675187087900672}\cdot t^{79}+\frac{789915089922976098994043888418379575}{2535301200456458802993406410752}\cdot t^{77}-\frac{160394972457642475062912728488006845}{2535301200456458802993406410752}\cdot t^{75}+\frac{978233073780127183076006201218063725}{81129638414606681695789005144064}\cdot t^{73}-\frac{87406382357343065317684764613119525}{40564819207303340847894502572032}\cdot t^{71}+\frac{7489822764068879907394711726331104125}{20769187434139310514121985316880384}\cdot t^{69}-\frac{1172502616075376502251968084210114125}{20769187434139310514121985316880384}\cdot t^{67}+\frac{2743283898563658673522858660516997175}{332306998946228968225951765070086144}\cdot t^{65}-\frac{23385370938575450987407975466702271}{20769187434139310514121985316880384}\cdot t^{63}+\frac{47525108681621077813119434012975583}{332306998946228968225951765070086144}\cdot t^{61}-\frac{5611753057643990992257618030955305}{332306998946228968225951765070086144}\cdot t^{59}+\frac{157405073469325714553324335261713555}{85070591730234615865843651857942052864}\cdot t^{57}-\frac{7985330491323707578738259347669893}{42535295865117307932921825928971026432}\cdot t^{55}+\frac{23955991473971122736214778043009679}{1361129467683753853853498429727072845824}\cdot t^{53}-\frac{2070196679489038450426687830381747}{1361129467683753853853498429727072845824}\cdot t^{51}+\frac{2631605948503014979355959106417475}{21778071482940061661655974875633165533184}\cdot t^{49}-\frac{47918502964194624298937939879025}{5444517870735015415413993718908291383296}\cdot t^{47}+\frac{51034385915560974253351638432735}{87112285931760246646623899502532662132736}\cdot t^{45}-\frac{3093940113680671433607968282205}{87112285931760246646623899502532662132736}\cdot t^{43}+\frac{5446058328759544453309932473355}{2787593149816327892691964784081045188247552}\cdot t^{41}-\frac{135342703042272592184329755975}{1393796574908163946345982392040522594123776}\cdot t^{39}+\frac{387215995962640891152850769025}{89202980794122492566142873090593446023921664}\cdot t^{37}-\frac{15488639838505635646114030761}{89202980794122492566142873090593446023921664}\cdot t^{35}+\frac{8818890625752012640610381151}{1427247692705959881058285969449495136382746624}\cdot t^{33}-\frac{34674537191685501863474631}{178405961588244985132285746181186892047843328}\cdot t^{31}+\frac{15312117563279922475323555}{2854495385411919762116571938898990272765493248}\cdot t^{29}-\frac{367722686069540312609805}{2854495385411919762116571938898990272765493248}\cdot t^{27}+\frac{487059104944938300852987}{182687704666362864775460604089535377456991567872}\cdot t^{25}-\frac{4295053835493283076305}{91343852333181432387730302044767688728495783936}\cdot t^{23}+\frac{2038740375947093092505}{2923003274661805836407369665432566039311865085952}\cdot t^{21}-\frac{25040091177265735725}{2923003274661805836407369665432566039311865085952}\cdot t^{19}+\frac{3997997750992008225}{46768052394588893382517914646921056628989841375232}\cdot t^{17}-\frac{7916827229687145}{11692013098647223345629478661730264157247460343808}\cdot t^{15}+\frac{773271496853163}{187072209578355573530071658587684226515959365500928}\cdot t^{13}-\frac{3501403503689}{187072209578355573530071658587684226515959365500928}\cdot t^{11}+\frac{357286071805}{5986310706507378352962293074805895248510699696029696}\cdot t^9-\frac{372474765}{2993155353253689176481146537402947624255349848014848}\cdot t^7+\frac{57940519}{383123885216472214589586756787577295904684780545900544}\cdot t^5-\frac{33511}{383123885216472214589586756787577295904684780545900544}\cdot t^3+\frac{93}{6129982163463555433433388108601236734474956488734408704}\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.