Rule: Q[31, 32]

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.

• $P_1$:
  $\frac{14544636039226909}{67108864}\cdot t^{31}-\frac{110873045217057585}{67108864}\cdot t^{29}+\frac{381478443712926945}{67108864}\cdot t^{27}-\frac{783034700252850045}{67108864}\cdot t^{25}+\frac{1067774591253886425}{67108864}\cdot t^{23}-\frac{1019422534291446285}{67108864}\cdot t^{21}+\frac{699603700003933725}{67108864}\cdot t^{19}-\frac{348782019535488825}{67108864}\cdot t^{17}+\frac{126155198555389575}{67108864}\cdot t^{15}-\frac{32706903329175075}{67108864}\cdot t^{13}+\frac{5932880138780595}{67108864}\cdot t^{11}-\frac{723521968143975}{67108864}\cdot t^9+\frac{55655536011075}{67108864}\cdot t^7-\frac{2429867476575}{67108864}\cdot t^5+\frac{49589132175}{67108864}\cdot t^3-\frac{300540195}{67108864}\cdot t$
• $P_2$:
  $\frac{14544636039226909}{67108864}\cdot t^{63}-\frac{14886315767820550977}{4362076160}\cdot t^{61}+\frac{486101674168742020046427}{18996841676800}\cdot t^{59}-\frac{3453077278507521203047883913}{28400278306816000}\cdot t^{57}+\frac{3609393116508948716398611339314373}{8781508053859041280000}\cdot t^{55}-\frac{43838871459399741166972590762677404737}{41668255715561150873600000}\cdot t^{53}+\frac{8844208875455680632750950037539751740666301}{4173700833749182677254144000000}\cdot t^{51}-\frac{934667182268995582949641037824071491160505353}{271290554193696874021519360000000}\cdot t^{49}+\frac{30503226372020988506576975619060785523074008102365927}{6626867268947501312614087602995200000000}\cdot t^{47}-\frac{456330454042665692239853548249776991964489561589544534717}{89164499103688630161222548698300416000000000}\cdot t^{45}+\frac{1249240163121932602528810759810557785945687039128206120622628317}{261419859311286797909946725029097185607680000000000}\cdot t^{43}-\frac{64078388774287272883473803706515560286576012021536047625351984601}{16992290855233641864146537126891317064499200000000000}\cdot t^{41}+\frac{26553892013479755248772679753306718828865240758396914433769423928588148021}{10513456689078928983439463454653179815549878747136000000000000}\cdot t^{39}-\frac{29179357659355960407513196258146364216906659588407871682292094042070416262219}{20273448982107201389732432028389548410985349517393920000000000000}\cdot t^{37}+\frac{61670091121986604489900838493091806433244601153369142974561865693433393063729369}{88290870317076862052284741483636483329841197148250521600000000000000}\cdot t^{35}-\frac{3272951474689491011900646626913038268404719841527441537811353655609357443822767564001}{11343203092165051273760466574037342880541852806607744591872000000000000000}\cdot t^{33}+\frac{738917050114573594550612272562809085271230616400509673460990571134865770193023156505577799737}{7296509358232191897427492907768125611387915329765356195604122654720000000000000000}\cdot t^{31}-\frac{1417003095629318915548211014932687458350154424011136359935494657081291186183829067484689911}{47074253924078657402758018759794358783147840837195846423252404224000000000000000}\cdot t^{29}+\frac{36727865198589072433735114486398485218230298586822527925197857436588565211364019858443889}{4869750405939171455457726078599416425842880086606466871370938368000000000000000}\cdot t^{27}-\frac{8593393563718956792093173635751936514725425975800515541309970835541938102462272611837}{5428930218438318233509170656186640385555050263775325386143744000000000000000}\cdot t^{25}+\frac{6892963244475030645848059663854422400317588065233862853481972626842754282333298147831}{24973079004816263874142185018458545773553231213366496776261222400000000000000}\cdot t^{23}-\frac{214862535709265351440768949945436388189792469532955642211278921559635730381465451801}{5428930218438318233509170656186640385555050263775325386143744000000000000000}\cdot t^{21}+\frac{5001083241930005618435091647313749744760515247798417391281523377242068728730039677}{1085786043687663646701834131237328077111010052755065077228748800000000000000}\cdot t^{19}-\frac{464657556009641084771264915902427459888052182661205135138952417435442419689707849}{1085786043687663646701834131237328077111010052755065077228748800000000000000}\cdot t^{17}+\frac{33748673281695561278888321562080710088092973629057729808024361410661536310109149}{1085786043687663646701834131237328077111010052755065077228748800000000000000}\cdot t^{15}-\frac{1864588689093025124082063675685699118591412330939450496865110977759435541748961}{1085786043687663646701834131237328077111010052755065077228748800000000000000}\cdot t^{13}+\frac{29066309333354046017930110545950412036547936667869198348275433410444726701409}{417610016802947556423782358168203106581157712598101952780288000000000000000}\cdot t^{11}-\frac{7149064257400753945546960753624744657572312468910186112764101716663359743}{3631391450460413534119846592766983535488327935635669154611200000000000000}\cdot t^9+\frac{39251638969336649545694595208207932796908898711454273222657311937771449869}{1085786043687663646701834131237328077111010052755065077228748800000000000000}\cdot t^7-\frac{5432572866118749916548676752124877511501132906893465771486775836283089037}{14115218567939627407123843706085265002443130685815846003973734400000000000000}\cdot t^5+\frac{27430684291383091147703369192276337005044837868757933086873249120259429}{14115218567939627407123843706085265002443130685815846003973734400000000000000}\cdot t^3-\frac{207347806955940399971668077662331256589084546342374615704456194136501}{70576092839698137035619218530426325012215653429079230019868672000000000000000}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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