Rule: Q[30, 31]

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.

• $P_1$:
  $\frac{7391536347803839}{67108864}\cdot t^{30}-\frac{54496920530418135}{67108864}\cdot t^{28}+\frac{180700315442965395}{67108864}\cdot t^{26}-\frac{355924863751295475}{67108864}\cdot t^{24}+\frac{463373879223384675}{67108864}\cdot t^{22}-\frac{419762220002360235}{67108864}\cdot t^{20}+\frac{271274904083157975}{67108864}\cdot t^{18}-\frac{126155198555389575}{67108864}\cdot t^{16}+\frac{42051732851796525}{67108864}\cdot t^{14}-\frac{9888133564634325}{67108864}\cdot t^{12}+\frac{1591748329916745}{67108864}\cdot t^{10}-\frac{166966608033225}{67108864}\cdot t^8+\frac{10529425731825}{67108864}\cdot t^6-\frac{347123925225}{67108864}\cdot t^4+\frac{4508102925}{67108864}\cdot t^2-\frac{9694845}{67108864}$
• $P_2$:
  $\frac{7391536347803839}{67108864}\cdot t^{61}-\frac{1014215431703863807}{603979776}\cdot t^{59}+\frac{30102688622807786158877}{2473297182720}\cdot t^{57}-\frac{582582527912478931894605113}{10439787408261120}\cdot t^{55}+\frac{178642174672327350198623068490237}{983271377047073587200}\cdot t^{53}-\frac{1965745486886597486165216118200452381}{4398172869531560155545600}\cdot t^{51}+\frac{76037585863691175375069293933854077716162717}{88089443052478934651567603712000}\cdot t^{49}-\frac{104925071461404497532222865640266980976566853}{78163872004312294127447310336000}\cdot t^{47}+\frac{894195427499707921176638058003530029435009383308411}{522692364215556892989947369603727360000}\cdot t^{45}-\frac{63059058097357603979368075152232499236911025041492369637}{34859294615791077195906971984137864347648000}\cdot t^{43}+\frac{81133568422029970212425339039794374925158408156314929229548013}{50675828065340883696619862847640816848784588800000}\cdot t^{41}-\frac{316172182479208779707251872049497534771680244765192266139567113689}{264983904953667480849625262830313831302294614835200000}\cdot t^{39}+\frac{91748131482672813964102532722538654534865900579536641305120124528016363647}{122067176949707190705573183761981172212101570096756948992000000}\cdot t^{37}-\frac{89429068780155120404514959550329930415872140099294023444724535824880516086661}{223016732287115037419082206733139601631509568566774945808384000000}\cdot t^{35}+\frac{14732179277003821828770790651240304075808721388879102166316860558520673695939619687}{81279563165700510962571605654926393512611819812003962874594590720000000}\cdot t^{33}-\frac{21377245576010556837719121536498839762408493581839392296634435329309551923711177227843}{308338652717619643428911988232032225293520872041509868833545917562880000000}\cdot t^{31}+\frac{626661997426210722063491972615662465372162061034127486429413766239006779535748461607}{27998567315737875667682812724517868733549596426757792687184054583296000000}\cdot t^{29}-\frac{2698799176573110699239593994255899893118211069547814767721466256129770814882123961}{444421703424410724883854170230442360849993594075520518844191342592000000}\cdot t^{27}+\frac{28235660623850722177169694115910654357925073041391026338467397258114477212920563}{20511770927280494994639423241405032039230473572716331638962677350400000}\cdot t^{25}-\frac{384494884902078451667390910127375713437843397064421805392898575569387017037067}{1486360212121774999611552408797466089799309679182342872388599808000000}\cdot t^{23}+\frac{1210192611128070922737205315099629534205099851385863447283681835341221001273}{30333881880036224481868416506070736526516524064945772905889792000000}\cdot t^{21}-\frac{4446263354279054180256465003834665799708548376863309328929298665101038333151}{891816127273064999766931445278479653879585807509405723433159884800000}\cdot t^{19}+\frac{104853538323052110000405022019778615258072710876966260459833384849028408697}{211106233025991231828887153713263299710626592115753045643598233600000}\cdot t^{17}-\frac{562746770374975001227769425981203584770955983461301651833553588366820949989}{14566330078793394996193213606215167680033234855986960149408278118400000}\cdot t^{15}+\frac{8224013728312290215667876862409230822142974109081723981423627255798395417}{3601565129371993268289530836701552448359865761095676960018530304000000}\cdot t^{13}-\frac{1543872287051530723760955704943278026747421198266770661509025206047814947}{15606782227278637495921300292373393942892751631414600160080297984000000}\cdot t^{11}+\frac{3109529984681243611735562228024159585344243160990799924192313057689307}{1040452148485242499728086686158226262859516775427640010672019865600000}\cdot t^9-\frac{67921054464376595533266008599527956160453872786141335746416473052819}{1159360965454984499697010878862023550043461549762227440463107850240000}\cdot t^7+\frac{4501131366518148162070921693376844471803957839627266382259919725057}{6762938965154076248232563460028470708586859040279660069368129126400000}\cdot t^5-\frac{848583642060299175746702639617271348460327311386428317432289861197}{236702863780392668688139721100996474800540066409788102427884519424000000}\cdot t^3+\frac{2052472381438583398985303596069590219151222536533041455914747063}{355054295670589003032209581651494712200810099614682153641826779136000000}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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