Rule: Q[32, 33]

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.

• $P_1$:
  $\frac{916312070471295267}{2147483648}\cdot t^{32}-\frac{450883717216034179}{134217728}\cdot t^{30}+\frac{3215318311294669965}{268435456}\cdot t^{28}-\frac{3433305993416342505}{134217728}\cdot t^{26}+\frac{19575867506321251125}{536870912}\cdot t^{24}-\frac{4911763119767877555}{134217728}\cdot t^{22}+\frac{7135957740040123995}{268435456}\cdot t^{20}-\frac{1898924328582105825}{134217728}\cdot t^{18}+\frac{5929294332103310025}{1073741824}\cdot t^{16}-\frac{210258664258982625}{134217728}\cdot t^{14}+\frac{85037948655855195}{268435456}\cdot t^{12}-\frac{5932880138780595}{134217728}\cdot t^{10}+\frac{2170565904431925}{536870912}\cdot t^8-\frac{29968365544425}{134217728}\cdot t^6+\frac{1735619626125}{268435456}\cdot t^4-\frac{9917826435}{134217728}\cdot t^2+\frac{300540195}{2147483648}$
• $P_2$:
  $\frac{916312070471295267}{2147483648}\cdot t^{65}-\frac{997398416389985284675}{143881404416}\cdot t^{63}+\frac{2977214558981356512773955}{55430311051264}\cdot t^{61}-\frac{69654400042478942293599091095}{263681989670862848}\cdot t^{59}+\frac{27466376755470819052310757998870205}{29662378064044374360064}\cdot t^{57}-\frac{24469492224051911644380965399877644247}{9936896651454865410621440}\cdot t^{55}+\frac{1122810037370072809536132757679296455510075}{217441159906465655888300474368}\cdot t^{53}-\frac{10083203397378215796785484321136200252731960487}{1150916059384922716616774410829824}\cdot t^{51}+\frac{792695778340922604536007508088729957608348577241261}{64735000134194055580185401898739695616}\cdot t^{49}-\frac{91264475772190739821429183687535774874414174906667973947}{6389846209495993289695045604270323189940224}\cdot t^{47}+\frac{248717933259133418622038162869495256082786089709778035267279557}{17724155415899986186956117497125022464256193331200}\cdot t^{45}-\frac{1789424290435386857248676468179496842610580141044780458414129003}{153057928769305214050025494652950749546887927300096}\cdot t^{43}+\frac{4513932128680338989314354721773575985393542551610349485801786380281114759}{544000990633131038377272120261972709990042919624293650268160}\cdot t^{41}-\frac{550155486840127631573928062144384687134552310030540360296544197461253917643}{109344199117259338713831696172656514707998626844483023703900160}\cdot t^{39}+\frac{4325783084984726439123790794241856378184473399875044451794238520134793850766769}{1657249225487618769904328765748007930783728473237092704832779714560}\cdot t^{37}-\frac{18953794993572198663974188621471174245801892339131786776911733929514357498944452272303}{16358334223712550163502400772726292982981757420416863743545781186985984000}\cdot t^{35}+\frac{211583978210104453811622148174396895822035685578946461111442270686294152099518968747480403}{481346197502899693045372396320676829727243999740253202384615198968697313034240}\cdot t^{33}-\frac{3274694862260960119011600808803684589767096162381833158492550463363078858442814304351329137}{23032156762235522946794700684161418196626191385420717748511157370007559602176000}\cdot t^{31}+\frac{1551288858946957468899860724228496844911483334649222068787085604253814683845556961398543}{39710615107302625770335690834761065856252054112794340945708892017254413107200}\cdot t^{29}-\frac{1080676661832337063104742193192791209726506596608826337265840670747826557594655261324359}{119131845321907877311007072504283197568756162338383022837126676051763239321600}\cdot t^{27}+\frac{70227364857860562584865433263878277974134615502565920226952721661506120204892071760921}{39710615107302625770335690834761065856252054112794340945708892017254413107200}\cdot t^{25}-\frac{9911173245748360917669319582856215030587631872129383531320847497356300138431642955}{34530969658524022408987557247618318135871351402429861691920775667177750528}\cdot t^{23}+\frac{66250889277724310517936619914130858078543873235310218011911102631449142814121300537}{1726548482926201120449377862380915906793567570121493084596038783358887526400}\cdot t^{21}-\frac{1439896031819025059971010050928056495509377566889204673433157861048463903532073187}{345309696585240224089875572476183181358713514024298616919207756671777505280}\cdot t^{19}+\frac{31270830624233249549630055337755300365986335969080431465492190096519116241162013}{86327424146310056022468893119045795339678378506074654229801939167944376320}\cdot t^{17}-\frac{85036540094755051409910241776807363990395190854480377846158766356463294103821383}{3453096965852402240898755724761831813587135140242986169192077566717775052800}\cdot t^{15}+\frac{1114364063048539617546917351488781145699494426146016568336664688163510439755}{874201763506937276176900183484008054072692440567844599795462675118424064}\cdot t^{13}-\frac{83638977367334827212803126512999270693152442505295262781298358061683172133339}{1726548482926201120449377862380915906793567570121493084596038783358887526400}\cdot t^{11}+\frac{443924315309364199318326888671394920883939393788638970322401368229422540467}{345309696585240224089875572476183181358713514024298616919207756671777505280}\cdot t^9-\frac{3826029138192385875079244594839656443449640489451648367228840836850190031}{172654848292620112044937786238091590679356757012149308459603878335888752640}\cdot t^7+\frac{382512572437821525698716049260982280915067826344136835045885197223346269}{1726548482926201120449377862380915906793567570121493084596038783358887526400}\cdot t^5-\frac{72565926143201767995730568921046624310223187731452728027279054203151}{69061939317048044817975114495236636271742702804859723383841551334355501056}\cdot t^3+\frac{10305227084816659926353855349491826393353046171694243382376236743101}{6906193931704804481797511449523663627174270280485972338384155133435550105600}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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