Rule: Q[41, 42]

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.

• $P_1$:
  $\frac{53098072606098965203605}{274877906944}\cdot t^{41}-\frac{134384010916670220577025}{68719476736}\cdot t^{39}+\frac{1260488001129780170222475}{137438953472}\cdot t^{37}-\frac{1817067118511761024606425}{68719476736}\cdot t^{35}+\frac{14415399140193304128544305}{274877906944}\cdot t^{33}-\frac{1303310059250353523950581}{17179869184}\cdot t^{31}+\frac{2845254354701476002990705}{34359738368}\cdot t^{29}-\frac{1195831540381779769372905}{17179869184}\cdot t^{27}+\frac{6264729413044846254475965}{137438953472}\cdot t^{25}-\frac{803170437569852083907175}{34359738368}\cdot t^{23}+\frac{645086097476738340407985}{68719476736}\cdot t^{21}-\frac{100944918383096163551175}{34359738368}\cdot t^{19}+\frac{97523056742991208854525}{137438953472}\cdot t^{17}-\frac{2237371072376316532425}{17179869184}\cdot t^{15}+\frac{610192110648086327025}{34359738368}\cdot t^{13}-\frac{29933952597830650005}{17179869184}\cdot t^{11}+\frac{32281713585895799025}{274877906944}\cdot t^9-\frac{348782019535488825}{68719476736}\cdot t^7+\frac{17315419409563275}{137438953472}\cdot t^5-\frac{101259762629025}{68719476736}\cdot t^3+\frac{1412926920405}{274877906944}\cdot t$
• $P_2$:
  $\frac{53098072606098965203605}{274877906944}\cdot t^{83}-\frac{18727624654995048115008763}{4672924418048}\cdot t^{81}+\frac{28848056352497815037836934241}{719922418155520}\cdot t^{79}-\frac{2801191953183511102637110167531969}{10892426186693017600}\cdot t^{77}+\frac{1662100603930968445392094328582660517981}{1396191188610310995968000}\cdot t^{75}-\frac{15579131424431275304684604544428820444642533}{3678963781988169474375680000}\cdot t^{73}+\frac{46167260278737729962236836371428751604003280845459}{3833769979229504160645565644800000}\cdot t^{71}-\frac{444443406119539677325006664951005685232774718732812297}{15804716739373630902261344370688000000}\cdot t^{69}+\frac{445430986270477964629557301927040752725121159152921295083837}{8103394366611648036207436485739151360000000}\cdot t^{67}-\frac{564848772798301240259478192274178378356208213700341913652791808779}{6191520016725128856784834958476284683878400000000}\cdot t^{65}+\frac{49474963682439753494014305181380020029654490131087913738119143681656613}{380717775109681440030429342384784572611035136000000000}\cdot t^{63}-\frac{20737118645757028969239107068389394873972322439835945205982650834626650831}{129444043537291689610345976410826754687751946240000000000}\cdot t^{61}+\frac{516433625610419144452930010739789303022187730565686178444308055095616434462303838203}{3002131582947880395067222642120349582548363858095269478400000000000}\cdot t^{59}-\frac{4497544893689947833437230124937161861953924346357425593451895260293598216198314801344481}{27814749116012111860297817779245038882310591145252671717376000000000000}\cdot t^{57}+\frac{632011909998657759192658135728956084252315049553303497221003414670498143422192925078661426429}{4732190129484823312215208839306466265621737195078243896661114880000000000000}\cdot t^{55}-\frac{39617852756830022036916394711391043959439875044068727836952593586787486953818704532410750243825278563}{407562873927374968771308977673871317599667953702061136437008028021555200000000000000}\cdot t^{53}+\frac{52214674652045833151673890706389959821573662223086737746040551504720355428168325581922384702347449666230767}{835862546880174775953702156131789207838807012888483143495931024508847128576000000000000000}\cdot t^{51}-\frac{2521365420509561633643835852357490527288594137814572779776996685861675751298332849231401931281022870985478901}{71048316484814855956064683271202082666298596095521067197154137083252005928960000000000000000}\cdot t^{49}+\frac{33336971141283780183525319167947992654945498817030781950220672021445645653399697845237356134757810980136148744794637}{1869458006010531541672179986575604476882900980685880726162778764908358380904441446400000000000000000}\cdot t^{47}-\frac{2518686681372943082824720071923593914042627077287352049255912982285332444311006835783159110050817918130529511895546147}{317807861021790362084270597717852761070093166716599723447672390034420924753755045888000000000000000000}\cdot t^{45}+\frac{16601556413505229391353794313670925975868978828884226499681775522133109314830459294412395063359990419877364323201252759925631839}{5332952037764832349457755806173395795807840101211574747777484280769130461226918693436995665920000000000000000000}\cdot t^{43}-\frac{4223895914172126167375311823880525790455289251218277871075437807869216591865242061835706069020196795975193569720502305592645361433361}{3913346870072022802193848499349068701942772105469559607792856852649791778100619071837534604630425600000000000000000000}\cdot t^{41}+\frac{121038716734006151253721938617399264451191012343861877619372160131020250241348271131314136019688104859349612747469992133496593317}{367105710138088442982537382678149033953355732220408968836102894244820992317131245012901932892160000000000000000000}\cdot t^{39}-\frac{855040740122829701802918409130468819182585162225742813451758097147345801722086855533695677977227356715327857995950312382069183}{9660676582581274815329931123109185104035677163694972864107970901179499797819243289813208760320000000000000000000}\cdot t^{37}+\frac{2997954369892906064727068017496239427798746333941686721760578705672072780171905723250517136927758442816870736887418095816991}{144054823225815840675935599226232023918518951182776855382784281844242308261983124545210941440000000000000000000}\cdot t^{35}-\frac{55217460941634517912421423646746225786984505404744893901636438178389053390172874492377326126350531254759866320931045989591}{12933714778788419131895146679754577998876314502478417356349053168678101980178051429755781120000000000000000000}\cdot t^{33}+\frac{1258504491945431495822089120980068679980510743997593525220918207107958049354642514223497522919852939415494015836979618307}{1655041627134832728354039513169026010093278391346241445114709120453151519554034059572736000000000000000000000}\cdot t^{31}-\frac{2562953651661375963740779751421303118373020983121437630754510355910291508793330298608190746435675776669398394555951179}{21922332714546456921389504256649388201064264161708707694354125946053734087155917888716800000000000000000000}\cdot t^{29}+\frac{3715554453319630422996926679822828738140660795459462783456016077089627098735582542146373080311209633591486271390327}{241133389798140766759984813082654551064197001949050589585770445760014791020233978675200000000000000000000}\cdot t^{27}-\frac{589950833517827944236963527028867473576857679007065052749576312209143412485617710581810074619219147289099147226956989}{341686013343965466498898480138121498857967151761804685443036721641940958875671547782758400000000000000000000}\cdot t^{25}+\frac{2782383148008367482701786539328848670258913160162412842679406760938185054465879891289923988127056885030287621283093}{17084300667198273324944924006906074942898357588090234272151836082097047943783577389137920000000000000000000}\cdot t^{23}-\frac{136445562687625492139604470150420829643244394491085519949066092717933608021514797017951728307152413846795791778841}{10677687916998920828090577504316296839311473492556396420094897551310654964864735868211200000000000000000000}\cdot t^{21}+\frac{449402516506322246649152484929492069246320132954589469438781303420514880742382990407611487949548248220158190350897}{546697621350344746398237568220994398172747442818887496708858754627105534201074476452413440000000000000000000}\cdot t^{19}-\frac{302689949652780134282362950158570030923263793842171448023995158160958715629643724377840377400591035640107061572867}{7107069077554481703177088386872927176245716756645537457215163810152371944613968193881374720000000000000000000}\cdot t^{17}+\frac{45415070347690080647643679684611887604997172865436407059871591649189749892566616734902249140458413557978575081}{26128930432185594496974589657621055795021017487667417122114572831442543914021941889269760000000000000000000}\cdot t^{15}-\frac{11490000104396303544087584892079017162875493852533916126456437540440649602735467117465052578786415452294711}{211570286900288214550401535689239318178307833908238195320765771914514525619610865500160000000000000000000}\cdot t^{13}+\frac{100624757753311630167003084210833068015326082032302365955835268875544045470347022324565444672196816806787433}{80396709022109521529152583561910940907756976885130514221890993327515519735452128890060800000000000000000000}\cdot t^{11}-\frac{105014058503182807282542065270758351947240704110171252119708384581091305581161550224606119023096379562127749}{5193627402828275090783256898099446782641100706779431218734158168957502574910207526297927680000000000000000000}\cdot t^9+\frac{4697313838330805739283811447114957699262212576415392517734450261842490574665344963865200190178200723687529}{22072916462020169135828841816922648826224678003812582679620172218069385943368381986766192640000000000000000000}\cdot t^7-\frac{14369044125191431076454991467409794283050876214054972422713123927271552692010073682093266673079040723347}{11036458231010084567914420908461324413112339001906291339810086109034692971684190993383096320000000000000000000}\cdot t^5+\frac{668226312720787979079968523531380638722987599826038190627815112195417147015244669507441804483203721923}{176583331696161353086630734535381190609797424030500661436961377744555087546947055894129541120000000000000000000}\cdot t^3-\frac{223838090152890407699345762001260290201184100162626819644244113765196577348318293628780860551611117}{67916666036985135802550282513608150234537470780961792860369760670982725979595021497742131200000000000000000000}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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