Rule: Q[35, 36]

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.

• $P_1$:
  $\frac{14023284727082855679}{4294967296}\cdot t^{35}-\frac{120925426269772451145}{4294967296}\cdot t^{33}+\frac{59560284580634192355}{536870912}\cdot t^{31}-\frac{142028370923050766385}{536870912}\cdot t^{29}+\frac{457646972974274691685}{1073741824}\cdot t^{27}-\frac{526669139390066940267}{1073741824}\cdot t^{25}+\frac{223164889572062262825}{536870912}\cdot t^{23}-\frac{141505556545693615275}{536870912}\cdot t^{21}+\frac{270146971587233265525}{2147483648}\cdot t^{19}-\frac{96845140757687397075}{2147483648}\cdot t^{17}+\frac{6456342717179159805}{536870912}\cdot t^{15}-\frac{1257729100749186975}{536870912}\cdot t^{13}+\frac{347882517228498525}{1073741824}\cdot t^{11}-\frac{32706903329175075}{1073741824}\cdot t^9+\frac{977947275623175}{536870912}\cdot t^7-\frac{33393321606645}{536870912}\cdot t^5+\frac{4281195077775}{4294967296}\cdot t^3-\frac{20419054425}{4294967296}\cdot t$
• $P_2$:
  $\frac{14023284727082855679}{4294967296}\cdot t^{71}-\frac{18167063745930570815799}{313532612608}\cdot t^{69}+\frac{281760631653411613035912033}{572197018009600}\cdot t^{67}-\frac{1225852512385670966780525614131}{459474205461708800}\cdot t^{65}+\frac{85713756889900086381070798495029163}{8280586696555233280000}\cdot t^{63}-\frac{18511665591800795145862289138987333859}{604482828848532029440000}\cdot t^{61}+\frac{506462708570242444153651311895925382644286591}{7050430810487016965275648000000}\cdot t^{59}-\frac{1199982919062857292734989747893476639827473005303}{8749584635814388053907079168000000}\cdot t^{57}+\frac{15884706251131149148529897620539071146521464156062548933}{73165339162375285064979082064691200000000}\cdot t^{55}-\frac{2114408302423389776763662707154208533384049099991621756267309}{7320470211484464296834404081084200386560000000}\cdot t^{53}+\frac{65365140074265324254073819965875345867322070682705018199899189069}{200397872039387210125841811719679985582080000000000}\cdot t^{51}-\frac{7827836817571215942479022102530539607229959986860581790887504771}{24850697814956066442806730227499359272960000000000}\cdot t^{49}+\frac{18215716826505430003723157720328074117368081452295087467013891421679114668807}{69644237325906419360999275716290329265961457549312000000000000}\cdot t^{47}-\frac{831996622120459984450835181922230391363049097712215520435334835322946810619968887}{4438357600542690199457122842123466393790457728160104448000000000000}\cdot t^{45}+\frac{1778717575340271516181752088542047882559412719956516547790666002531412580944047916661}{15300004950759662604239692908542282763038772335129693388800000000000000}\cdot t^{43}-\frac{542668075209572383200195216412322738466372447365338192282312900344494281390371108766639981}{8686134110650226413341562697730533312515134868872164660382924800000000000000}\cdot t^{41}+\frac{76843443486020752239978623207513432900470220822477787430158336971424522566595467177770582490010457}{2640487025081470747990371987113371782826796050413584218809377888993280000000000000000}\cdot t^{39}-\frac{12826753032128570833650992148767742390277314461189294194683094858409262096498900664134774353740716667}{1092281466042035066085350545335898127496017966187752671847479320080220160000000000000000}\cdot t^{37}+\frac{51434577834805381910543931620794064536146483108981425005832209354296477720445517002595603032228625758425395471}{12550565426811038809299546393305190768304594043073467204499559030835215721275392000000000000000000}\cdot t^{35}-\frac{2264129981863074845784647631695049916985936620854890880354386801079187324208953833533166268408378823506608083}{1835124692659765338502622749945464868642856607978809490405817875096913895379763200000000000000000}\cdot t^{33}+\frac{4438590165428096095721604967794119248875329930321913125747618212805956327119163469827221120279558250515073}{13902459792877010140171384469283824762445883393778859775801650568916014358937600000000000000000}\cdot t^{31}-\frac{31697928448916060823544128559751309758526923962437641363279465368102336952018616662476161520589856967551}{448466444931516456134560789331736282659544625605769670187150018352129495449600000000000000000}\cdot t^{29}+\frac{5556326997940102311764271863903357226425768403856567731251077441437278181230273856304689017561884342939}{417537724591411872952866941791616539027851892805371761898381051569224013004800000000000000000}\cdot t^{27}-\frac{163536974705962204408049145805323365562886962405605731850637221341924693012473090295640669472594175477}{77321800850261457954234618850299359079231832000994770721922416957263706112000000000000000000}\cdot t^{25}+\frac{1739410083150268138036679589252304104607663021803423777905695120603359050685376385242179810031764587}{6185744068020916636338769508023948726338546560079581657753793356581096488960000000000000000}\cdot t^{23}-\frac{21482570033699257789954046287616661563484832754187108173573634140006436977344866840026086239961637}{694655750954220584829487484858304402423045335623910239640800323466326343680000000000000000}\cdot t^{21}+\frac{17164290925600720780720988605816973206139755135028025015997271693301411296024319162184984226201941}{6185744068020916636338769508023948726338546560079581657753793356581096488960000000000000000}\cdot t^{19}-\frac{1235063890594792486660623581072719918704088750765019466838574781271202965767506425450143247155493}{6185744068020916636338769508023948726338546560079581657753793356581096488960000000000000000}\cdot t^{17}+\frac{523054567844083531575735337421491378246123346511991002822976128558419941330645084867486415880971}{46393080510156874772540771310179615447539099200596862433153450174358223667200000000000000000}\cdot t^{15}-\frac{16530056179627732429473352734882366165921861484192992669195009100374384319623751341825428258903}{34021592374115041499863232294131717994862006080437699117645863461196030689280000000000000000}\cdot t^{13}+\frac{524019835147226732172090989244000119148862851625849938141328108625764484345037946201293704381}{34021592374115041499863232294131717994862006080437699117645863461196030689280000000000000000}\cdot t^{11}-\frac{161611189963000744589607188882962846122856214681140165631621732768076235524412510027256895119}{473209421203600122679915867363832077564898811846087996818165191778453881405440000000000000000}\cdot t^9+\frac{3500169259637926159803571665848976806659444896015769177536975901434795355690027705943183749}{710720663263644628699337241404682660557242659937419520125366878073386672455680000000000000000}\cdot t^7-\frac{35703991366515943438900721938999930518654315907179333241146785166474440852307328355282963}{866004169522928329087427731123352821687396518411141432085531069921353508454400000000000000000}\cdot t^5+\frac{1447186051922408985130744937241131241492999815982272626800742200523891616168268547262099}{8833242529133868956691762857458198781211444487793642607272416913197805786234880000000000000000}\cdot t^3-\frac{574188451136698433010708526189445796070077008181790591239762496347435004098846602881}{2944414176377956318897254285819399593737148162597880869090805637732601928744960000000000000000}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.