Rule: Q[1, 96, 98]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{97}-48\cdot t^{95}+\frac{4465}{8}\cdot t^{93}-\frac{33511}{8}\cdot t^{91}+\frac{2919735}{128}\cdot t^{89}-\frac{6147141}{64}\cdot t^{87}+\frac{333281949}{1024}\cdot t^{85}-\frac{933921945}{1024}\cdot t^{83}+\frac{70625252863}{32768}\cdot t^{81}-\frac{35709397515}{8192}\cdot t^{79}+\frac{2000375522613}{262144}\cdot t^{77}-\frac{3058045339167}{262144}\cdot t^{75}+\frac{65783533458825}{4194304}\cdot t^{73}-\frac{39112924418505}{2097152}\cdot t^{71}+\frac{661194674693775}{33554432}\cdot t^{69}-\frac{622956910374135}{33554432}\cdot t^{67}+\frac{33594090947249085}{2147483648}\cdot t^{65}-\frac{1585777713559325}{134217728}\cdot t^{63}+\frac{68822752768474705}{8589934592}\cdot t^{61}-\frac{41953909915492575}{8589934592}\cdot t^{59}+\frac{368118665976450235}{137438953472}\cdot t^{57}-\frac{90834476020163045}{68719476736}\cdot t^{55}+\frac{645402855932737425}{1099511627776}\cdot t^{53}-\frac{257786995789945557}{1099511627776}\cdot t^{51}+\frac{2961066843533158425}{35184372088832}\cdot t^{49}-\frac{238507849862670843}{8796093022208}\cdot t^{47}+\frac{2203649450440574199}{281474976710656}\cdot t^{45}-\frac{569017463728786765}{281474976710656}\cdot t^{43}+\frac{2097235794886099791}{4503599627370496}\cdot t^{41}-\frac{214859239356147155}{2251799813685248}\cdot t^{39}+\frac{624355672011392321}{36028797018963968}\cdot t^{37}-\frac{100101318622914609}{36028797018963968}\cdot t^{35}+\frac{1804857108504066435}{4611686018427387904}\cdot t^{33}-\frac{27767032438524099}{576460752303423488}\cdot t^{31}+\frac{759510004936100355}{147573952589676412928}\cdot t^{29}-\frac{69923143311577493}{147573952589676412928}\cdot t^{27}+\frac{87967825456500717}{2361183241434822606848}\cdot t^{25}-\frac{2923166552608575}{1180591620717411303424}\cdot t^{23}+\frac{2594951360736735}{18889465931478580854784}\cdot t^{21}-\frac{118413686604675}{18889465931478580854784}\cdot t^{19}+\frac{139646485582065}{604462909807314587353088}\cdot t^{17}-\frac{1015828093665}{151115727451828646838272}\cdot t^{15}+\frac{725591495475}{4835703278458516698824704}\cdot t^{13}-\frac{11965356585}{4835703278458516698824704}\cdot t^{11}+\frac{2215806775}{77371252455336267181195264}\cdot t^9-\frac{8361535}{38685626227668133590597632}\cdot t^7+\frac{587265}{618970019642690137449562112}\cdot t^5-\frac{1225}{618970019642690137449562112}\cdot t^3+\frac{49}{39614081257132168796771975168}\cdot t$
• $P_3$:
  $2\cdot t^{195}-97\cdot t^{193}+2316\cdot t^{191}-36290\cdot t^{189}+\frac{53727345}{128}\cdot t^{187}-\frac{978400269}{256}\cdot t^{185}+\frac{14607344367}{512}\cdot t^{183}-\frac{183867048937}{1024}\cdot t^{181}+\frac{31863768374295}{32768}\cdot t^{179}-\frac{301617168134815}{65536}\cdot t^{177}+\frac{1262900271738677}{65536}\cdot t^{175}-\frac{9448479920010495}{131072}\cdot t^{173}+\frac{1018655682970406845}{4194304}\cdot t^{171}-\frac{6223690774264339425}{8388608}\cdot t^{169}+\frac{34674848599472748225}{16777216}\cdot t^{167}-\frac{177026915814840428415}{33554432}\cdot t^{165}+\frac{26613046344164344405055}{2147483648}\cdot t^{163}-\frac{115468961840947038836655}{4294967296}\cdot t^{161}+\frac{116045585870115313687275}{2147483648}\cdot t^{159}-\frac{433436992005506528464425}{4294967296}\cdot t^{157}+\frac{48253358219085754068866805}{274877906944}\cdot t^{155}-\frac{156708525263888020356986481}{549755813888}\cdot t^{153}+\frac{476020567337641039893165831}{1099511627776}\cdot t^{151}-\frac{1354846173686550584767555425}{2199023255552}\cdot t^{149}+\frac{57901294228945374990880101225}{70368744177664}\cdot t^{147}-\frac{145342406636447443047282892689}{140737488355328}\cdot t^{145}+\frac{171648724579695849028691561049}{140737488355328}\cdot t^{143}-\frac{381930637882457145559567262619}{281474976710656}\cdot t^{141}+\frac{12821957128911061315214043816495}{9007199254740992}\cdot t^{139}-\frac{25392399509268219920342327946315}{18014398509481984}\cdot t^{137}+\frac{47501123258703360798776933162223}{36028797018963968}\cdot t^{135}-\frac{83997587463337614550329884741409}{72057594037927936}\cdot t^{133}+\frac{8991839301868019274668240588537661}{9223372036854775808}\cdot t^{131}-\frac{14234153496078487474214550773637885}{18446744073709551616}\cdot t^{129}+\frac{1333482789392973772094173601887645}{2305843009213693952}\cdot t^{127}-\frac{1893379910902073318638062642183327}{4611686018427387904}\cdot t^{125}+\frac{163041047883234091327166505299119825}{590295810358705651712}\cdot t^{123}-\frac{207937613848020633559022656681845325}{1180591620717411303424}\cdot t^{121}+\frac{251436888163995636182295883995702375}{2361183241434822606848}\cdot t^{119}-\frac{288312655854877243448619859796476625}{4722366482869645213696}\cdot t^{117}+\frac{5016640211874864036005985560458693275}{151115727451828646838272}\cdot t^{115}-\frac{5174520312956685091427102336554954275}{302231454903657293676544}\cdot t^{113}+\frac{2531258854390066733035768675457618325}{302231454903657293676544}\cdot t^{111}-\frac{2348888175414403010363788989765733375}{604462909807314587353088}\cdot t^{109}+\frac{33075492345667885452156129171677288625}{19342813113834066795298816}\cdot t^{107}-\frac{27604285076126943105103371380806755525}{38685626227668133590597632}\cdot t^{105}+\frac{21843390799370015848386146049160128285}{77371252455336267181195264}\cdot t^{103}-\frac{16384882460244280058770873225223212035}{154742504910672534362390528}\cdot t^{101}+\frac{372719173082133397733301395438636129625}{9903520314283042199192993792}\cdot t^{99}-\frac{251014953300212288269366245907652903625}{19807040628566084398385987584}\cdot t^{97}+\frac{40024850087869466239115384963905202715}{9903520314283042199192993792}\cdot t^{95}-\frac{24166457828578386309350938994433634905}{19807040628566084398385987584}\cdot t^{93}+\frac{441812421327599729194031269308491838135}{1267650600228229401496703205376}\cdot t^{91}-\frac{238715116154706543218044339334776893675}{2535301200456458802993406410752}\cdot t^{89}+\frac{121910327968418208560493170687922054725}{5070602400912917605986812821504}\cdot t^{87}-\frac{58809353569291104864578330308641702995}{10141204801825835211973625643008}\cdot t^{85}+\frac{428468147433406621156213549391532407535}{324518553658426726783156020576256}\cdot t^{83}-\frac{184030935973227657679489424281128964135}{649037107316853453566312041152512}\cdot t^{81}+\frac{37247640714221489935129043894981124675}{649037107316853453566312041152512}\cdot t^{79}-\frac{14197696528580528329844436996218835225}{1298074214633706907132624082305024}\cdot t^{77}+\frac{81455804005150246849264358139090807585}{41538374868278621028243970633760768}\cdot t^{75}-\frac{27448677123775584093103654382025135525}{83076749736557242056487941267521536}\cdot t^{73}+\frac{8682609952007972435806018742893844025}{166153499473114484112975882535043072}\cdot t^{71}-\frac{2575043051765104607110389852737940375}{332306998946228968225951765070086144}\cdot t^{69}+\frac{91531075749105081943651130220048607875}{85070591730234615865843651857942052864}\cdot t^{67}-\frac{23766906456990174536396083255023778275}{170141183460469231731687303715884105728}\cdot t^{65}+\frac{720209286575459834436244947121932675}{42535295865117307932921825928971026432}\cdot t^{63}-\frac{162740800264014006323497209502387425}{85070591730234615865843651857942052864}\cdot t^{61}+\frac{8759284249504283281529408629099087875}{43556142965880123323311949751266331066368}\cdot t^{59}-\frac{1710274489433051317436587717036236375}{87112285931760246646623899502532662132736}\cdot t^{57}+\frac{309478240945028333631382539273223725}{174224571863520493293247799005065324265472}\cdot t^{55}-\frac{51783119752492064838603162909378843}{348449143727040986586495598010130648530944}\cdot t^{53}+\frac{127880177453286855461640068976924813}{11150372599265311570767859136324180752990208}\cdot t^{51}-\frac{18158728839841935707048790282389925}{22300745198530623141535718272648361505980416}\cdot t^{49}+\frac{1182690801708801306573403709132175}{22300745198530623141535718272648361505980416}\cdot t^{47}-\frac{140880303762778425609459990035469}{44601490397061246283071436545296723011960832}\cdot t^{45}+\frac{244686843377457265532219982693183}{1427247692705959881058285969449495136382746624}\cdot t^{43}-\frac{24113523908091663295383023504523}{2854495385411919762116571938898990272765493248}\cdot t^{41}+\frac{2148314820147236408323998182715}{5708990770823839524233143877797980545530986496}\cdot t^{39}-\frac{172227770391550598135679179205}{11417981541647679048466287755595961091061972992}\cdot t^{37}+\frac{395529983037147235718490804657}{730750818665451459101842416358141509827966271488}\cdot t^{35}-\frac{25264663436081868518787120641}{1461501637330902918203684832716283019655932542976}\cdot t^{33}+\frac{356753912447882610663232769}{730750818665451459101842416358141509827966271488}\cdot t^{31}-\frac{17687447413185351738821115}{1461501637330902918203684832716283019655932542976}\cdot t^{29}+\frac{24425522618208342877419635}{93536104789177786765035829293842113257979682750464}\cdot t^{27}-\frac{908676040168641054581271}{187072209578355573530071658587684226515959365500928}\cdot t^{25}+\frac{28816364910210604267905}{374144419156711147060143317175368453031918731001856}\cdot t^{23}-\frac{768801046323239784855}{748288838313422294120286634350736906063837462003712}\cdot t^{21}+\frac{271798349710236287575}{23945242826029513411849172299223580994042798784118784}\cdot t^{19}-\frac{4880554216155665775}{47890485652059026823698344598447161988085597568237568}\cdot t^{17}+\frac{34788017473646255}{47890485652059026823698344598447161988085597568237568}\cdot t^{15}-\frac{382285906303805}{95780971304118053647396689196894323976171195136475136}\cdot t^{13}+\frac{49863379083105}{3064991081731777716716694054300618367237478244367204352}\cdot t^{11}-\frac{286301894725}{6129982163463555433433388108601236734474956488734408704}\cdot t^9+\frac{1074975825}{12259964326927110866866776217202473468949912977468817408}\cdot t^7-\frac{2352735}{24519928653854221733733552434404946937899825954937634816}\cdot t^5+\frac{156849}{3138550867693340381917894711603833208051177722232017256448}\cdot t^3-\frac{49}{6277101735386680763835789423207666416102355444464034512896}\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.