Rule: Q[34, 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.

• $P_1$:
  $\frac{7113260368810144185}{4294967296}\cdot t^{34}-\frac{59560284580634192355}{4294967296}\cdot t^{32}+\frac{28405674184610153277}{536870912}\cdot t^{30}-\frac{65378138996324955955}{536870912}\cdot t^{28}+\frac{202565053611564207795}{1073741824}\cdot t^{26}-\frac{223164889572062262825}{1073741824}\cdot t^{24}+\frac{90048990529077755175}{536870912}\cdot t^{22}-\frac{54029394317446653105}{536870912}\cdot t^{20}+\frac{96845140757687397075}{2147483648}\cdot t^{18}-\frac{32281713585895799025}{2147483648}\cdot t^{16}+\frac{1976431444034436675}{536870912}\cdot t^{14}-\frac{347882517228498525}{536870912}\cdot t^{12}+\frac{85037948655855195}{1073741824}\cdot t^{10}-\frac{6845630929362225}{1073741824}\cdot t^8+\frac{166966608033225}{536870912}\cdot t^6-\frac{4281195077775}{536870912}\cdot t^4+\frac{347123925225}{4294967296}\cdot t^2-\frac{583401555}{4294967296}$
• $P_2$:
  $\frac{7113260368810144185}{4294967296}\cdot t^{70}-\frac{8710134237575418493755}{304942678016}\cdot t^{68}+\frac{372364875759478920694336863}{1580517900156928}\cdot t^{66}-\frac{138836583081902647093087598845}{112216770911141888}\cdot t^{64}+\frac{3715313293871594261198081855589555}{799726844994616557568}\cdot t^{62}-\frac{59574543452636153607578293309595719143}{4485667873574804271398912}\cdot t^{60}+\frac{698680911777189792077705171040366925742327}{23249216588738210538660560896}\cdot t^{58}-\frac{37844888063015916024844963093673644229317035963}{685038166787171373521633426800640}\cdot t^{56}+\frac{22319035023048495031133746076598205603551086538808455}{265581350820651610326404428622857240576}\cdot t^{54}-\frac{175868163849035470672233847471072374410435007759571349491}{1640496004019164996986200155603389175037952}\cdot t^{52}+\frac{397899344405320052609176422926256736299755225254365001991655163}{3435771203234086008805579976037231379797287895040}\cdot t^{50}-\frac{754909657996760976352533435387643851504468840934566495761079209581}{7074252907458983092130689170660659411002615775887360}\cdot t^{48}+\frac{23717092840345904835944102773310446254089553077305100273898247290116571737}{281318755756538904614573769726596132062145762928389573836800}\cdot t^{46}-\frac{25438405328611970202511323835997387591326644739532215437760993147201102343}{443858481304761382836327503346407230586941092620347994275840}\cdot t^{44}+\frac{5142938812452858009151632275670269477191293447715696944761453952676411242388757}{153070037295531879905245938485103266706939366646658873396895416320}\cdot t^{42}-\frac{26496044781202095615774050055373460983931683357224972480520203873432984049072925423719}{1558304258131008540615171911167743764670989577150813961902983298102067200}\cdot t^{40}+\frac{1510654413774237716324155886284507224760297373587415133558940401452079071418537555669201357851}{203392616464492556137468441368406786284208400112699459941235611856197534718361600}\cdot t^{38}-\frac{20803263184514034821884796051655485186863014561332466615815065363810849692540746022609031777401347}{7437051021024170315166533558635794140482080150120855752751280147521862856976891904000}\cdot t^{36}+\frac{1823628040338114928570698333356785913988711806930643555059858446868983757629299226202316933255886040471}{2012113490070743941611125087276166557772192038023587838131815997240423552798526244546150400}\cdot t^{34}-\frac{903155482582969045458956731836901326350796299353641048062420167630129741041919506587141258314418339}{3586655062514695083085784469297979603872000067778231440520171118075621306236232164966400}\cdot t^{32}+\frac{8638066195518629652003780462549342790599395689642627737159824138969508015003868573647545465601607}{144623188004624801737330018923305629188387099507186751633877867664339568799848071168000}\cdot t^{30}-\frac{323859471840564688931460941180937081294326985879867403435411950310111343315922939280702542769553}{26929835007757721702813175937443117159216908184096843407687602944394264535144123596800}\cdot t^{28}+\frac{2035439657838268133012187396929201871138455998705974151699482292952014713842440055165843253661}{997401296583619322326413923609004339230255858670253459543985294236824612412745318400}\cdot t^{26}-\frac{57703563300303724570005904344948573015672220156652393307335371120700135240150301416115681533}{199480259316723864465282784721800867846051171734050691908797058847364922482549063680}\cdot t^{24}+\frac{476991393739565245826474107916955540815963142979294359688840010437553407771499352375057697}{14080959481180508079902314215656531847956553298874166487679792389225759234062286848}\cdot t^{22}-\frac{586260947690190672584524531020259803700026910700459234184697245489520580594669942491975133}{181345690287930785877529804292546243496410156121864265371633689861240838620499148800}\cdot t^{20}+\frac{98615862708955459854414758166831196966570551466832448406070057607998987642852454976563473}{398960518633447728930565569443601735692102343468101383817594117694729844965098127360}\cdot t^{18}-\frac{975518262833330078300195927715165747572425604480069274429734508282036682308996235002488521}{65828485574518875273543318958194286389196886672236728329903029419630424419241191014400}\cdot t^{16}+\frac{1486758384075251324132326574794708302745042431217450009058674607702941712873989826248051}{2194282852483962509118110631939809546306562889074557610996767647321014147308039700480}\cdot t^{14}-\frac{49975354096653080881979968712424494413048761910909788638512855852486074910249239942991}{2194282852483962509118110631939809546306562889074557610996767647321014147308039700480}\cdot t^{12}+\frac{4804316237022452849023549033276021381168329378029328050308567104077245548519028066207}{8976611669252573900937725312481039053072302728032281135895867648131421511714707865600}\cdot t^{10}-\frac{19188339001776995365887173769869088058339300174555804151092314568750073978839339}{2346826580196751346650385702609421974659425549812361081279965398204293205677047808}\cdot t^8+\frac{578454888249783016230301874596198092037743344169182936530364849807320730576550073}{7979210372668954578611311388872034713842046869362027676351882353894596899301962547200}\cdot t^6-\frac{24829888964972504590700994317639320725886626426304074360659769370301099793322123}{81387945801223336701835376166494754081188878067492682298789200009724888372880017981440}\cdot t^4+\frac{10439237063496991870543532760642102545962481966732095655994259606928685067067}{27129315267074445567278458722164918027062959355830894099596400003241629457626672660480}\cdot t^2-\frac{83535771471890932905628909194548804937961095723352627136186083122037123}{135646576335372227836392293610824590135314796779154470497982000016208147288133363302400}$

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.