Rule: Q[29, 58, 88]

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.

• $P_1$:
  $268435456\cdot t^{29}-1946157056\cdot t^{27}+6325010432\cdot t^{25}-12163481600\cdot t^{23}+15386804224\cdot t^{21}-13463453696\cdot t^{19}+8341487616\cdot t^{17}-3683254272\cdot t^{15}+1151016960\cdot t^{13}-249387008\cdot t^{11}+36095488\cdot t^9-3281408\cdot t^7+168896\cdot t^5-4060\cdot t^3+29\cdot t$
• $P_2$:
  $268435456\cdot t^{87}-5838471168\cdot t^{85}+61303947264\cdot t^{83}-413923278848\cdot t^{81}+2019746119680\cdot t^{79}-7588826578944\cdot t^{77}+22844554084352\cdot t^{75}-56601462128640\cdot t^{73}+117680888033280\cdot t^{71}-208288466355200\cdot t^{69}+317301780564480\cdot t^{67}-419589854562240\cdot t^{65}+484859387494144\cdot t^{63}-492167559135168\cdot t^{61}+440639253041760\cdot t^{59}-349043408312246\cdot t^{57}+\frac{980762816313987}{4}\cdot t^{55}-\frac{2447786188615581}{16}\cdot t^{53}+\frac{2715820747111329}{32}\cdot t^{51}-\frac{10720345054386825}{256}\cdot t^{49}+\frac{4704151411924965}{256}\cdot t^{47}-\frac{7337933154820905}{1024}\cdot t^{45}+\frac{5080107568722165}{2048}\cdot t^{43}-\frac{199449440632874565}{262144}\cdot t^{41}+\frac{216334049363699925}{1048576}\cdot t^{39}-\frac{206843265262582767}{4194304}\cdot t^{37}+\frac{86858521226280027}{8388608}\cdot t^{35}-\frac{127606963283053373}{67108864}\cdot t^{33}+\frac{10196198034723393}{33554432}\cdot t^{31}-\frac{5637612468663945}{134217728}\cdot t^{29}+\frac{1338520855133077}{268435456}\cdot t^{27}-\frac{2165072903924931}{4294967296}\cdot t^{25}+\frac{2952372141715815}{68719476736}\cdot t^{23}-\frac{838327892092145}{274877906944}\cdot t^{21}+\frac{97696369222725}{549755813888}\cdot t^{19}-\frac{36716657444145}{4398046511104}\cdot t^{17}+\frac{1359876201635}{4398046511104}\cdot t^{15}-\frac{154364325591}{17592186044416}\cdot t^{13}+\frac{6466389579}{35184372088832}\cdot t^{11}-\frac{3039755785}{1125899906842624}\cdot t^9+\frac{116416179}{4503599627370496}\cdot t^7-\frac{2592513}{18014398509481984}\cdot t^5+\frac{13717}{36028797018963968}\cdot t^3-\frac{87}{288230376151711744}\cdot t$
• $P_3$:
  $268435456\cdot t^{175}-11811160064\cdot t^{173}+255399559168\cdot t^{171}-3617922744320\cdot t^{169}+37762247950336\cdot t^{167}-309697118732288\cdot t^{165}+2078336660471808\cdot t^{163}-11735875064365056\cdot t^{161}+56908184481054720\cdot t^{159}-240665565632790528\cdot t^{157}+898474642228859904\cdot t^{155}-2990125507693169664\cdot t^{153}+8942102382294809728\cdot t^{151}-24190791380363206400\cdot t^{149}+59533511546828725165\cdot t^{147}-133922874827581602945\cdot t^{145}+\frac{4424249651286642901395}{16}\cdot t^{143}-\frac{2103618079531470737235}{4}\cdot t^{141}+\frac{236596526447127239371825}{256}\cdot t^{139}-\frac{385237362407355362404115}{256}\cdot t^{137}+\frac{4660565261557908401362685}{2048}\cdot t^{135}-\frac{3279803949566479013288505}{1024}\cdot t^{133}+\frac{275485411299774477563674815}{65536}\cdot t^{131}-\frac{337691330473400456934155775}{65536}\cdot t^{129}+\frac{387193920667675121469652911}{65536}\cdot t^{127}-\frac{25987707725860186825705641}{4096}\cdot t^{125}+\frac{6699093041626993306970621055}{1048576}\cdot t^{123}-\frac{6331568163017255475012306785}{1048576}\cdot t^{121}+\frac{44974716544656178390085336075}{8388608}\cdot t^{119}-\frac{18772099083378100818654942305}{4194304}\cdot t^{117}+\frac{1887097502511497783823411719195}{536870912}\cdot t^{115}-\frac{1395117307734705731878479052495}{536870912}\cdot t^{113}+\frac{31083525650086091970855653186755}{17179869184}\cdot t^{111}-\frac{5097583113238504014652676367525}{4294967296}\cdot t^{109}+\frac{201696801297848575706834519818365}{274877906944}\cdot t^{107}-\frac{117548536905722548804153021279695}{274877906944}\cdot t^{105}+\frac{516725248821061406514429152982585}{2199023255552}\cdot t^{103}-\frac{133861660414485564393954321213585}{1099511627776}\cdot t^{101}+\frac{4185491493369664068169130833763625}{70368744177664}\cdot t^{99}-\frac{1928060998417450838950634839715425}{70368744177664}\cdot t^{97}+\frac{3349425697251386834273684325096725}{281474976710656}\cdot t^{95}-\frac{171398781319020818693843459071325}{35184372088832}\cdot t^{93}+\frac{8464019577658196476277192193486825}{4503599627370496}\cdot t^{91}-\frac{3076324990560382551798943235475375}{4503599627370496}\cdot t^{89}+\frac{8423842772658001700755993222621725}{36028797018963968}\cdot t^{87}-\frac{1357085269371621511065294826304275}{18014398509481984}\cdot t^{85}+\frac{421258717846920313981569532574022725}{18446744073709551616}\cdot t^{83}-\frac{120074465931172609841641290404518825}{18446744073709551616}\cdot t^{81}+\frac{514570949335713353792121076878955125}{295147905179352825856}\cdot t^{79}-\frac{32352829278799928497977976845501969}{73786976294838206464}\cdot t^{77}+\frac{488558145553671625882511614873338447}{4722366482869645213696}\cdot t^{75}-\frac{108055118202259424477944448527444989}{4722366482869645213696}\cdot t^{73}+\frac{179035394995729842640125312944380419}{37778931862957161709568}\cdot t^{71}-\frac{17342649093555076638252978035106255}{18889465931478580854784}\cdot t^{69}+\frac{200904558679721339431240684184908701}{1208925819614629174706176}\cdot t^{67}-\frac{33932062619994578142705712690238733}{1208925819614629174706176}\cdot t^{65}+\frac{10680090455826813189034586909899281}{2417851639229258349412352}\cdot t^{63}-\frac{48866119369339999700972264016081}{75557863725914323419136}\cdot t^{61}+\frac{3402391545700685313094976296169865}{38685626227668133590597632}\cdot t^{59}-\frac{428968909985007843198922691060871}{38685626227668133590597632}\cdot t^{57}+\frac{400344583405499209589710653387549}{309485009821345068724781056}\cdot t^{55}-\frac{21560732027967205201208972535567}{154742504910672534362390528}\cdot t^{53}+\frac{273813174594821325148000183837827}{19807040628566084398385987584}\cdot t^{51}-\frac{24959872278127507993219583353575}{19807040628566084398385987584}\cdot t^{49}+\frac{133413062969571293920746145684455}{1267650600228229401496703205376}\cdot t^{47}-\frac{2544283848563195847423761955285}{316912650057057350374175801344}\cdot t^{45}+\frac{11307182310281291659658987827665}{20282409603651670423947251286016}\cdot t^{43}-\frac{712073655563378439788215513755}{20282409603651670423947251286016}\cdot t^{41}+\frac{324007700678520111639944771325}{162259276829213363391578010288128}\cdot t^{39}-\frac{8284122360811646591539305645}{81129638414606681695789005144064}\cdot t^{37}+\frac{24249940497453570261840163665}{5192296858534827628530496329220096}\cdot t^{35}-\frac{986446227252773283256641465}{5192296858534827628530496329220096}\cdot t^{33}+\frac{141832581140529353256946995}{20769187434139310514121985316880384}\cdot t^{31}-\frac{559031244193066369788525}{2596148429267413814265248164610048}\cdot t^{29}+\frac{1962825563853006260954007}{332306998946228968225951765070086144}\cdot t^{27}-\frac{46390996669988729588193}{332306998946228968225951765070086144}\cdot t^{25}+\frac{7473888489473250997347}{2658455991569831745807614120560689152}\cdot t^{23}-\frac{63287219444593098357}{1329227995784915872903807060280344576}\cdot t^{21}+\frac{227169892631700948105}{340282366920938463463374607431768211456}\cdot t^{19}-\frac{2587840575373799469}{340282366920938463463374607431768211456}\cdot t^{17}+\frac{374386256739994707}{5444517870735015415413993718908291383296}\cdot t^{15}-\frac{652262733055003}{1361129467683753853853498429727072845824}\cdot t^{13}+\frac{215792719675169}{87112285931760246646623899502532662132736}\cdot t^{11}-\frac{785635893955}{87112285931760246646623899502532662132736}\cdot t^9+\frac{14963504941}{696898287454081973172991196020261297061888}\cdot t^7-\frac{10383769}{348449143727040986586495598010130648530944}\cdot t^5+\frac{439031}{22300745198530623141535718272648361505980416}\cdot t^3-\frac{87}{22300745198530623141535718272648361505980416}\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.