Rule: Q[16, 35]

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.

• $P_1$:
  $\frac{300540195}{32768}\cdot t^{16}-\frac{145422675}{4096}\cdot t^{14}+\frac{456326325}{8192}\cdot t^{12}-\frac{185910725}{4096}\cdot t^{10}+\frac{334639305}{16384}\cdot t^8-\frac{20369349}{4096}\cdot t^6+\frac{4849845}{8192}\cdot t^4-\frac{109395}{4096}\cdot t^2+\frac{6435}{32768}$
• $P_2$:
  $\frac{300540195}{32768}\cdot t^{51}-\frac{576132468831188433041942014748342027348561465444434783453890719377226604481731}{4979812163762315293157980539312803766648878312336354456663808606980243456}\cdot t^{49}+\frac{104563353304025858433785356267669362822972571241325577677867256368593089829257419531}{152413376037150362441216441881342500282997231846944548589266692177389076275200}\cdot t^{47}-\frac{1007348273358722766874544465475058571175936199159134932088619178312403994431862857641}{396274777696590942347162748891490500735792802802055826332093399661211598315520}\cdot t^{45}+\frac{413158076790748143163390289167430498615824348178381953549925447086359763364248679652711}{62611414876061368890851714324855499116255262842724820560470757146471432533852160}\cdot t^{43}-\frac{96612567548056676214998828297800181922996931522908200807761312781986764365791196408402121}{7575981200003425635793057433307515393066886803969703287816961614723043336596111360}\cdot t^{41}+\frac{27729519499241598107214131804465856638352333201929799375740856946461521613347674457301357}{1456919461539120314575587967943752960205170539224942939964800310523662180114636800}\cdot t^{39}-\frac{633047784017312073185580180937627323359320689021980095892645976802302537281148238627582055343}{28184106983474282485464749239871901015169024081306521173619062007080244874317648896000}\cdot t^{37}+\frac{647436290922409306613417882340429497305528197524499187273947171116964433172192560563341123383653}{30416288256565445658313557379669755575570410788545997650569691718041000268363606688563200}\cdot t^{35}-\frac{45240240422748251178629370299980581573772545607336108370316287091842390133913757796624056675441}{2765117114233222332573959761788159597779128253504181604597244701640090933487600608051200}\cdot t^{33}+\frac{7414962187850916073883203109532301994086620166414840863913470685214448604345007598309151881051}{722701063947319473286375846830996258510453975347683828474279865201387403070622886195200}\cdot t^{31}-\frac{41839917839230232340029851356117553829184044688785217950564730553283546715685255795949335125963}{7949711703420514206150134315140958843614993728824522113217078517215261433776851748147200}\cdot t^{29}+\frac{175518346913897966563389397152746506714332495889846635372716544267536943931049922194515557130753}{79497117034205142061501343151409588436149937288245221132170785172152614337768517481472000}\cdot t^{27}-\frac{2401491838194663267735839503917726670150795267879499393799916139708943695728222753873312857807}{3179884681368205682460053726056383537445997491529808845286831406886104573510740699258880}\cdot t^{25}+\frac{20313471467229426299587081039936140948373517908725541511859508774799867266884315428942745676389}{96986482781730273315031638644719697892102923491659169781248357910026189492077591327395840}\cdot t^{23}-\frac{20064133101024767785069937767928362342523517709202498604947949736963733812352069386340887628163}{429730621337231764372136232888263957853942202506521459781736795324661495733671857225338880}\cdot t^{21}+\frac{8939361029685360148967567905200085206215318502525161090037629911887783838730877072546966807001629}{1081546027781544904571792470933182729126801735268413209978675166473108052462505330264732893184}\cdot t^{19}-\frac{1155261444479091283305687293373103222378177393019626571913694641049284635116145962835120842853153883}{1010676301224280514772219753758876808191913937352140870693230398985791235340620112571070132551680}\cdot t^{17}+\frac{6105131969845221965957013311496519718238276237282187315294987655442180862942926661710002223788077}{50533815061214025738610987687943840409595696867607043534661519949289561767031005628553506627584}\cdot t^{15}-\frac{7520645677050392544129115025866542523937168976234179978630512212635858295085576649359683651}{793795495848541897529272045490077762045768945941896035793680902739346880618133639568236544}\cdot t^{13}+\frac{374075272280656353426553721598642223456827278268817566042541201263119190235486525440684370173}{706766644212783576763790037593620145588751005141357252233028251039014849888545533266482610176}\cdot t^{11}-\frac{6384517558577852672416311174214375096938226341327764932072784165610224225277324898633446981}{321257565551265262165359107997100066176705002336980569196831023199552204494793424212037550080}\cdot t^9+\frac{4057938445994567404506587844791297231248352739456610941473270674226016981696790382775263427}{8834583052659794709547375469920251819859387564266965652912853137987685623606819165831032627200}\cdot t^7-\frac{9974535936392255503230827234636453474921527803747955246766941987693280672881079293073661}{1766916610531958941909475093984050363971877512853393130582570627597537124721363833166206525440}\cdot t^5+\frac{195337458530035268636777689150093530911239231847327732992789362911271365799021801077613}{7067666442127835767637900375936201455887510051413572522330282510390148498885455332664826101760}\cdot t^3-\frac{159242934662834566380754281890662418805616832000170935902646703083377488943922698163}{7067666442127835767637900375936201455887510051413572522330282510390148498885455332664826101760}\cdot t$

Warning: This rule has negative weights!

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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