Rule: Q[5, 6, 40, 50, 100]

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.

• $P_1$:
  $16\cdot t^5-20\cdot t^3+5\cdot t$
• $P_2$:
  $16\cdot t^{11}-48\cdot t^9+53\cdot t^7-26\cdot t^5+\frac{85}{16}\cdot t^3-\frac{5}{16}\cdot t$
• $P_3$:
  $16\cdot t^{51}-208\cdot t^{49}+1273\cdot t^{47}-4876\cdot t^{45}+\frac{209715}{16}\cdot t^{43}-\frac{420497}{16}\cdot t^{41}+\frac{5220243}{128}\cdot t^{39}-\frac{3210259}{64}\cdot t^{37}+\frac{203461557}{4096}\cdot t^{35}-\frac{163907965}{4096}\cdot t^{33}+\frac{432375229}{16384}\cdot t^{31}-\frac{29267999}{2048}\cdot t^{29}+\frac{1666443037}{262144}\cdot t^{27}-\frac{607545099}{262144}\cdot t^{25}+\frac{1445389725}{2097152}\cdot t^{23}-\frac{173996955}{1048576}\cdot t^{21}+\frac{4295336595}{134217728}\cdot t^{19}-\frac{654116895}{134217728}\cdot t^{17}+\frac{2469143955}{4294967296}\cdot t^{15}-\frac{54977475}{1073741824}\cdot t^{13}+\frac{228524205}{68719476736}\cdot t^{11}-\frac{10311015}{68719476736}\cdot t^9+\frac{2408445}{549755813888}\cdot t^7-\frac{20345}{274877906944}\cdot t^5+\frac{10425}{17592186044416}\cdot t^3-\frac{25}{17592186044416}\cdot t$
• $P_4$:
  $16\cdot t^{101}-408\cdot t^{99}+5048\cdot t^{97}-40376\cdot t^{95}+\frac{3755065}{16}\cdot t^{93}-\frac{33812599}{32}\cdot t^{91}+\frac{245452389}{64}\cdot t^{89}-\frac{1476192003}{128}\cdot t^{87}+\frac{120029113347}{4096}\cdot t^{85}-\frac{523100058305}{8192}\cdot t^{83}+\frac{494376770041}{4096}\cdot t^{81}-\frac{3271630074147}{16384}\cdot t^{79}+\frac{152695331559459}{524288}\cdot t^{77}-\frac{394958317266261}{1048576}\cdot t^{75}+\frac{910126028842425}{2097152}\cdot t^{73}-\frac{1875557851877835}{4194304}\cdot t^{71}+\frac{110948466413615445}{268435456}\cdot t^{69}-\frac{184431889994883615}{536870912}\cdot t^{67}+\frac{138109040560912905}{536870912}\cdot t^{65}-\frac{46655249572613825}{268435456}\cdot t^{63}+\frac{1821991823291725085}{17179869184}\cdot t^{61}-\frac{2009392504428687235}{34359738368}\cdot t^{59}+\frac{2003139234339385045}{68719476736}\cdot t^{57}-\frac{1804841545270196155}{137438953472}\cdot t^{55}+\frac{23505759086361871725}{4398046511104}\cdot t^{53}-\frac{17271728717926352319}{8796093022208}\cdot t^{51}+\frac{1430423059799094993}{2199023255552}\cdot t^{49}-\frac{3413176438348135739}{17592186044416}\cdot t^{47}+\frac{29277056984424771501}{562949953421312}\cdot t^{45}-\frac{14074072341784425355}{1125899906842624}\cdot t^{43}+\frac{6050645799039207443}{2251799813685248}\cdot t^{41}-\frac{2319093596405381873}{4503599627370496}\cdot t^{39}+\frac{50532528421825268819}{576460752303423488}\cdot t^{37}-\frac{15218433803974624041}{1152921504606846976}\cdot t^{35}+\frac{2017193238916309545}{1152921504606846976}\cdot t^{33}-\frac{234036416267560263}{1152921504606846976}\cdot t^{31}+\frac{6044735182142233619}{295147905179352825856}\cdot t^{29}-\frac{1052626779041855773}{590295810358705651712}\cdot t^{27}+\frac{156790448502127167}{1180591620717411303424}\cdot t^{25}-\frac{19767864500838825}{2361183241434822606848}\cdot t^{23}+\frac{33335144403310365}{75557863725914323419136}\cdot t^{21}-\frac{2893337347330815}{151115727451828646838272}\cdot t^{19}+\frac{50765795571645}{75557863725914323419136}\cdot t^{17}-\frac{5632614911385}{302231454903657293676544}\cdot t^{15}+\frac{3839652247725}{9671406556917033397649408}\cdot t^{13}-\frac{120983049915}{19342813113834066795298816}\cdot t^{11}+\frac{2678236015}{38685626227668133590597632}\cdot t^9-\frac{38698205}{77371252455336267181195264}\cdot t^7+\frac{10416665}{4951760157141521099596496896}\cdot t^5-\frac{41675}{9903520314283042199192993792}\cdot t^3+\frac{25}{9903520314283042199192993792}\cdot t$
• $P_5$:
  $16\cdot t^{201}-808\cdot t^{199}+20098\cdot t^{197}-328251\cdot t^{195}+3959540\cdot t^{193}-\frac{75239699}{2}\cdot t^{191}+\frac{2345629553}{8}\cdot t^{189}-\frac{30844101231}{16}\cdot t^{187}+\frac{44698589013177}{4096}\cdot t^{185}-\frac{442543409354805}{8192}\cdot t^{183}+\frac{7757166927603093}{32768}\cdot t^{181}-\frac{60778239222115103}{65536}\cdot t^{179}+\frac{858342137078056527}{262144}\cdot t^{177}-\frac{5499330143432580083}{524288}\cdot t^{175}+\frac{64303481720817213325}{2097152}\cdot t^{173}-\frac{344742187565270545115}{4194304}\cdot t^{171}+\frac{54462806686641604097955}{268435456}\cdot t^{169}-\frac{248510288558871448771935}{536870912}\cdot t^{167}+\frac{2102826368412569321898155}{2147483648}\cdot t^{165}-\frac{8272702533083037151670425}{4294967296}\cdot t^{163}+\frac{30338625652350347999368845}{8589934592}\cdot t^{161}-\frac{103948400683237112347811895}{17179869184}\cdot t^{159}+\frac{666818607277541616405214005}{68719476736}\cdot t^{157}-\frac{2005761227669947586833620795}{137438953472}\cdot t^{155}+\frac{181345211399742352411133268675}{8796093022208}\cdot t^{153}-\frac{481960476156158560695310987239}{17592186044416}\cdot t^{151}+\frac{2412878205985128330195864623103}{70368744177664}\cdot t^{149}-\frac{5695369253501730145214046688461}{140737488355328}\cdot t^{147}+\frac{25379552625516798745446969880503}{562949953421312}\cdot t^{145}-\frac{53427975157511659879157782768515}{1125899906842624}\cdot t^{143}+\frac{212716550983391563222217902852053}{4503599627370496}\cdot t^{141}-\frac{400726808307188571022294664621283}{9007199254740992}\cdot t^{139}+\frac{45752134650421023892128377858521749}{1152921504606846976}\cdot t^{137}-\frac{77337261344955257395280261558753961}{2305843009213693952}\cdot t^{135}+\frac{247866998535195966701017568708987205}{9223372036854775808}\cdot t^{133}-\frac{376739061842182535095235454228130119}{18446744073709551616}\cdot t^{131}+\frac{271661012409471054780989972664157887}{18446744073709551616}\cdot t^{129}-\frac{185932808364726714367358026851001077}{18446744073709551616}\cdot t^{127}+\frac{483292479166690420569085415609655991}{73786976294838206464}\cdot t^{125}-\frac{596485111716372890198469428238983625}{147573952589676412928}\cdot t^{123}+\frac{44752047022457201859773625127733666525}{18889465931478580854784}\cdot t^{121}-\frac{49836426595978172461322473774673386025}{37778931862957161709568}\cdot t^{119}+\frac{105450303650235662788328628595150211225}{151115727451828646838272}\cdot t^{117}-\frac{105991717485168456657664425980030803275}{302231454903657293676544}\cdot t^{115}+\frac{202430381134629364366475441603765922375}{1208925819614629174706176}\cdot t^{113}-\frac{183643810994082438406835341345797286075}{2417851639229258349412352}\cdot t^{111}+\frac{316513145844240097030514709412234897525}{9671406556917033397649408}\cdot t^{109}-\frac{259060419614469812570041120512144078675}{19342813113834066795298816}\cdot t^{107}+\frac{6443238496478655329530793496925570176525}{1237940039285380274899124224}\cdot t^{105}-\frac{4754470570106037644116268068081955408625}{2475880078570760549798248448}\cdot t^{103}+\frac{6659730218483914892731298668937834665845}{9903520314283042199192993792}\cdot t^{101}-\frac{4425577077896384508567162994069963717095}{19807040628566084398385987584}\cdot t^{99}+\frac{2789423545298304771560955547509894176265}{39614081257132168796771975168}\cdot t^{97}-\frac{1666911590794868973157314292754852292735}{79228162514264337593543950336}\cdot t^{95}+\frac{1887972853211684624356316020183583657725}{316912650057057350374175801344}\cdot t^{93}-\frac{1012707831390707441017079107294307478035}{633825300114114700748351602688}\cdot t^{91}+\frac{16455681282186294544818055446862826650445}{40564819207303340847894502572032}\cdot t^{89}-\frac{7905438958598379446189814902117090168265}{81129638414606681695789005144064}\cdot t^{87}+\frac{7181343274446385690135637556929279172545}{324518553658426726783156020576256}\cdot t^{85}-\frac{3081634367866863261565603894485112166675}{649037107316853453566312041152512}\cdot t^{83}+\frac{2496732972966998023210980716445263965205}{2596148429267413814265248164610048}\cdot t^{81}-\frac{954005327161019285725544370328708831305}{5192296858534827628530496329220096}\cdot t^{79}+\frac{687036871081234582306697118079357020495}{20769187434139310514121985316880384}\cdot t^{77}-\frac{232901119441886995492584498405650514105}{41538374868278621028243970633760768}\cdot t^{75}+\frac{9503946339607735072973931207343126993875}{10633823966279326983230456482242756608}\cdot t^{73}-\frac{2846168023450095667726991509018275227775}{21267647932558653966460912964485513216}\cdot t^{71}+\frac{1599361040180713300220743634311655562675}{85070591730234615865843651857942052864}\cdot t^{69}-\frac{421042948445883376940795199012223596225}{170141183460469231731687303715884105728}\cdot t^{67}+\frac{25926901999520263030192582587217388475}{85070591730234615865843651857942052864}\cdot t^{65}-\frac{11931688033751286232946615577190303875}{340282366920938463463374607431768211456}\cdot t^{63}+\frac{5121191956864911344770365786346776225}{1361129467683753853853498429727072845824}\cdot t^{61}-\frac{1023180848764011838251261338653518975}{2722258935367507707706996859454145691648}\cdot t^{59}+\frac{48627084051468525338405290713098829075}{1393796574908163946345982392040522594123776}\cdot t^{57}-\frac{8370720648242827911142173798605819175}{2787593149816327892691964784081045188247552}\cdot t^{55}+\frac{2666216103509518312296543822306606375}{11150372599265311570767859136324180752990208}\cdot t^{53}-\frac{391878648197280748854496427590524501}{22300745198530623141535718272648361505980416}\cdot t^{51}+\frac{106031478220830666746200170990025677}{89202980794122492566142873090593446023921664}\cdot t^{49}-\frac{13165113632075963018935292873503449}{178405961588244985132285746181186892047843328}\cdot t^{47}+\frac{2990915737547893388575157810429127}{713623846352979940529142984724747568191373312}\cdot t^{45}-\frac{309745652528488720976528299137585}{1427247692705959881058285969449495136382746624}\cdot t^{43}+\frac{932287846286261226901243225198077}{91343852333181432387730302044767688728495783936}\cdot t^{41}-\frac{79306758827539428468074669716097}{182687704666362864775460604089535377456991567872}\cdot t^{39}+\frac{12146211815738422318493315859413}{730750818665451459101842416358141509827966271488}\cdot t^{37}-\frac{832970133263615293346589184807}{1461501637330902918203684832716283019655932542976}\cdot t^{35}+\frac{50861296128512908980245849055}{2923003274661805836407369665432566039311865085952}\cdot t^{33}-\frac{2747153216467409913861850229}{5846006549323611672814739330865132078623730171904}\cdot t^{31}+\frac{260579849492583897831975343}{23384026197294446691258957323460528314494920687616}\cdot t^{29}-\frac{10760872019458229042378081}{46768052394588893382517914646921056628989841375232}\cdot t^{27}+\frac{12262588792859759003761293}{2993155353253689176481146537402947624255349848014848}\cdot t^{25}-\frac{372364896176045720008425}{5986310706507378352962293074805895248510699696029696}\cdot t^{23}+\frac{19031032506243957125745}{23945242826029513411849172299223580994042798784118784}\cdot t^{21}-\frac{402895160836062566595}{47890485652059026823698344598447161988085597568237568}\cdot t^{19}+\frac{13867075140656890705}{191561942608236107294793378393788647952342390272950272}\cdot t^{17}-\frac{189511401941688645}{383123885216472214589586756787577295904684780545900544}\cdot t^{15}+\frac{3993918630494275}{1532495540865888858358347027150309183618739122183602176}\cdot t^{13}-\frac{31229080858885}{3064991081731777716716694054300618367237478244367204352}\cdot t^{11}+\frac{11009702491865}{392318858461667547739736838950479151006397215279002157056}\cdot t^9-\frac{39668649405}{784637716923335095479473677900958302012794430558004314112}\cdot t^7+\frac{166666665}{3138550867693340381917894711603833208051177722232017256448}\cdot t^5-\frac{166675}{6277101735386680763835789423207666416102355444464034512896}\cdot t^3+\frac{25}{6277101735386680763835789423207666416102355444464034512896}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.