Rule: Q[1, 36, 38, 74]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{37}-\frac{37}{4}\cdot t^{35}+\frac{629}{16}\cdot t^{33}-\frac{407}{4}\cdot t^{31}+\frac{5735}{32}\cdot t^{29}-\frac{232841}{1024}\cdot t^{27}+\frac{878787}{4096}\cdot t^{25}-\frac{627705}{4096}\cdot t^{23}+\frac{5476185}{65536}\cdot t^{21}-\frac{9126975}{262144}\cdot t^{19}+\frac{11560835}{1048576}\cdot t^{17}-\frac{1374365}{524288}\cdot t^{15}+\frac{1924111}{4194304}\cdot t^{13}-\frac{1924111}{33554432}\cdot t^{11}+\frac{657305}{134217728}\cdot t^9-\frac{35853}{134217728}\cdot t^7+\frac{35853}{4294967296}\cdot t^5-\frac{2109}{17179869184}\cdot t^3+\frac{37}{68719476736}\cdot t$
• $P_3$:
  $t^{75}-19\cdot t^{73}+\frac{2773}{16}\cdot t^{71}-\frac{8085}{8}\cdot t^{69}+\frac{1083461}{256}\cdot t^{67}-\frac{3470533}{256}\cdot t^{65}+\frac{8843263}{256}\cdot t^{63}-\frac{2300727}{32}\cdot t^{61}+\frac{1020317415}{8192}\cdot t^{59}-\frac{1491565961}{8192}\cdot t^{57}+\frac{237967863049}{1048576}\cdot t^{55}-\frac{127436677887}{524288}\cdot t^{53}+\frac{3775144262643}{16777216}\cdot t^{51}-\frac{3033774827175}{16777216}\cdot t^{49}+\frac{8491494002145}{67108864}\cdot t^{47}-\frac{1296042427365}{16777216}\cdot t^{45}+\frac{176912705973465}{4294967296}\cdot t^{43}-\frac{82401584774355}{4294967296}\cdot t^{41}+\frac{536069842313775}{68719476736}\cdot t^{39}-\frac{94996094126115}{34359738368}\cdot t^{37}+\frac{936954702926515}{1099511627776}\cdot t^{35}-\frac{250352961919515}{1099511627776}\cdot t^{33}+\frac{115505564632885}{2199023255552}\cdot t^{31}-\frac{715187791675}{68719476736}\cdot t^{29}+\frac{123844579170319}{70368744177664}\cdot t^{27}-\frac{17736182025705}{70368744177664}\cdot t^{25}+\frac{68191278865263}{2251799813685248}\cdot t^{23}-\frac{3397580313853}{1125899906842624}\cdot t^{21}+\frac{8860027645865}{36028797018963968}\cdot t^{19}-\frac{580273254077}{36028797018963968}\cdot t^{17}+\frac{119527914549}{144115188075855872}\cdot t^{15}-\frac{1176468391}{36028797018963968}\cdot t^{13}+\frac{17472589069}{18446744073709551616}\cdot t^{11}-\frac{355004455}{18446744073709551616}\cdot t^9+\frac{75149997}{295147905179352825856}\cdot t^7-\frac{288933}{147573952589676412928}\cdot t^5+\frac{33781}{4722366482869645213696}\cdot t^3-\frac{37}{4722366482869645213696}\cdot t$
• $P_4$:
  $t^{149}-\frac{75}{2}\cdot t^{147}+689\cdot t^{145}-\frac{33069}{4}\cdot t^{143}+\frac{18651061}{256}\cdot t^{141}-\frac{257439539}{512}\cdot t^{139}+\frac{2897744815}{1024}\cdot t^{137}-\frac{27348471149}{2048}\cdot t^{135}+\frac{3533492463093}{65536}\cdot t^{133}-\frac{24791512166751}{131072}\cdot t^{131}+\frac{76478465517597}{131072}\cdot t^{129}-\frac{52368023732505}{32768}\cdot t^{127}+\frac{4107436462339119}{1048576}\cdot t^{125}-\frac{18136605348075025}{2097152}\cdot t^{123}+\frac{72530167225891175}{4194304}\cdot t^{121}-\frac{263920399155094825}{8388608}\cdot t^{119}+\frac{28072982387270866375}{536870912}\cdot t^{117}-\frac{85534780301637906525}{1073741824}\cdot t^{115}+\frac{3743520002627402525}{33554432}\cdot t^{113}-\frac{309252942919506772725}{2147483648}\cdot t^{111}+\frac{188781769029332414422025}{1099511627776}\cdot t^{109}-\frac{416598624734726954235375}{2199023255552}\cdot t^{107}+\frac{852206393551287676478775}{4398046511104}\cdot t^{105}-\frac{1618304020274578665195453}{8796093022208}\cdot t^{103}+\frac{45699883954211404580004771}{281474976710656}\cdot t^{101}-\frac{75045020286641520965512377}{562949953421312}\cdot t^{99}+\frac{57378673008338778216091125}{562949953421312}\cdot t^{97}-\frac{40883197841967220966746653}{562949953421312}\cdot t^{95}+\frac{869175628542634304633117649}{18014398509481984}\cdot t^{93}-\frac{1077367501341820030573762783}{36028797018963968}\cdot t^{91}+\frac{1246163484192923295081872517}{72057594037927936}\cdot t^{89}-\frac{1345335651645686192849459795}{144115188075855872}\cdot t^{87}+\frac{86766257384759206300141790233}{18446744073709551616}\cdot t^{85}-\frac{81614588643211278468124248371}{36893488147419103232}\cdot t^{83}+\frac{17912098844776309259449692343}{18446744073709551616}\cdot t^{81}-\frac{29345092536004301707012362609}{73786976294838206464}\cdot t^{79}+\frac{717492095868255482203161121935}{4722366482869645213696}\cdot t^{77}-\frac{511125114670685976321763015113}{9444732965739290427392}\cdot t^{75}+\frac{339292612730263007335528249605}{18889465931478580854784}\cdot t^{73}-\frac{209734141999461149736815167935}{37778931862957161709568}\cdot t^{71}+\frac{1930155207250019138664380738115}{1208925819614629174706176}\cdot t^{69}-\frac{1032079312094433587686178574825}{2417851639229258349412352}\cdot t^{67}+\frac{256257819837065108832120199695}{2417851639229258349412352}\cdot t^{65}-\frac{29510948984098742779342218495}{1208925819614629174706176}\cdot t^{63}+\frac{201502222801037803472799948165}{38685626227668133590597632}\cdot t^{61}-\frac{79550267559489793723076001435}{77371252455336267181195264}\cdot t^{59}+\frac{29006417881938516658992591525}{154742504910672534362390528}\cdot t^{57}-\frac{9751427576607324176000164635}{309485009821345068724781056}\cdot t^{55}+\frac{96530339936820523504953556143}{19807040628566084398385987584}\cdot t^{53}-\frac{27418406839885575119732540661}{39614081257132168796771975168}\cdot t^{51}+\frac{891716429064329991595565001}{9903520314283042199192993792}\cdot t^{49}-\frac{847837460710475756541741825}{79228162514264337593543950336}\cdot t^{47}+\frac{11749086999167733881694398511}{10141204801825835211973625643008}\cdot t^{45}-\frac{2309937677472362108307173433}{20282409603651670423947251286016}\cdot t^{43}+\frac{410891180316291819699515961}{40564819207303340847894502572032}\cdot t^{41}-\frac{65865114295822954906583139}{81129638414606681695789005144064}\cdot t^{39}+\frac{151557767240244541129603065}{2596148429267413814265248164610048}\cdot t^{37}-\frac{19457927849207012684915259}{5192296858534827628530496329220096}\cdot t^{35}+\frac{1108851685705090491011499}{5192296858534827628530496329220096}\cdot t^{33}-\frac{55743697379890545622509}{5192296858534827628530496329220096}\cdot t^{31}+\frac{78540775008928734228261}{166153499473114484112975882535043072}\cdot t^{29}-\frac{6008035951969101709995}{332306998946228968225951765070086144}\cdot t^{27}+\frac{395466672212916774561}{664613997892457936451903530140172288}\cdot t^{25}-\frac{22152974938455094695}{1329227995784915872903807060280344576}\cdot t^{23}+\frac{133433129080635343245}{340282366920938463463374607431768211456}\cdot t^{21}-\frac{5193401467418192655}{680564733841876926926749214863536422912}\cdot t^{19}+\frac{41019522814377225}{340282366920938463463374607431768211456}\cdot t^{17}-\frac{2055701529897665}{1361129467683753853853498429727072845824}\cdot t^{15}+\frac{1269582144831245}{87112285931760246646623899502532662132736}\cdot t^{13}-\frac{18165175252315}{174224571863520493293247799005065324265472}\cdot t^{11}+\frac{182965834535}{348449143727040986586495598010130648530944}\cdot t^9-\frac{1204713525}{696898287454081973172991196020261297061888}\cdot t^7+\frac{73966885}{22300745198530623141535718272648361505980416}\cdot t^5-\frac{135087}{44601490397061246283071436545296723011960832}\cdot t^3+\frac{37}{44601490397061246283071436545296723011960832}\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.