Rule: Q[9, 48]

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.

• $P_1$:
  $\frac{12155}{128}\cdot t^9-\frac{6435}{32}\cdot t^7+\frac{9009}{64}\cdot t^5-\frac{1155}{32}\cdot t^3+\frac{315}{128}\cdot t$
• $P_2$:
  $\frac{12155}{128}\cdot t^{57}-\frac{1394211432516252569910273160746690302818646725382685693692465346585}{1032829841885593414646397974945683397712270870106636886399048864}\cdot t^{55}+\frac{1100761613262378791260174089490612910751080651594440874945699793381810268987}{121102754809736777062855569410005546638412504778334551737310370521498944}\cdot t^{53}-\frac{29008493263300801978775078788499887913636464919063230219312651050406652588620523}{752229761500679990725927369390249452944499273430625068116303366494290690656}\cdot t^{51}+\frac{34226067013893334229851435349372709820091360941385613884823125473205925694659562463}{295877039523600796352198098626831451491503047549379193459079324154421004991360}\cdot t^{49}-\frac{57317884309944317676105495335383997067668904563925687449601056712872531329684743667}{219643414544305693210432772194918245877620884787932003307632865635042123603280}\cdot t^{47}+\frac{57564801447110285157571402480287254705923022725281697285986337393787163180121180789331}{125196746290254245129946680151103400150243904329121241885350733411974010453869600}\cdot t^{45}-\frac{20984391231156804046030500106269511756376042652803071087225558415821155998820119153}{32350580436758202875955214509329043966471293108300062502674608116789149988080}\cdot t^{43}+\frac{1895779481025731971734717975576286946649532878257311754788010198207733078828088110159}{2543860276295327952977551501904313115802523145881936622161535038256785842965120}\cdot t^{41}-\frac{838573597700938883204830999668655701533805517916821725473645944239062268931447131215599}{1188618714098991986028760939264790303358728939913334886704977246625483185125452320}\cdot t^{39}+\frac{51610800292796916129034845829700010442831945247810125373372971101809151604673423946761}{93036282615035809972561584989686690411344505418317710430349096227095849847876160}\cdot t^{37}-\frac{84697161958539574993654641513868039018885221845553441032520877190298743835263313274327}{232590706537589524931403962474216726028361263545794276075872740567739624619690400}\cdot t^{35}+\frac{1324472996265231301912578220577443853839623668191282814337191968208918769107870011036351}{6618866963183976195190809903551995974978509099760317113473407131584819032034618240}\cdot t^{33}-\frac{1229289575529866634395587568527802774259102262658810729490184005044422560907801911917}{13344489845128984264497600611999991885037316733387736115873804700775844822650440}\cdot t^{31}+\frac{673379890739007369469601479085887811168050198365165189587105918401886854107831487278379}{18975864559773415624115588070263988460523064394877360756772550284503251337808925680}\cdot t^{29}-\frac{11193957042244950844590378995652229636686922771522728009607405287354916555130362420997}{981510235850349084005978693289516644509813675597104866729614669888099207128047880}\cdot t^{27}+\frac{309756608696988034573117480074301784894486797076191616472562232910512168467922674042837}{101786246680776942045064457081875800171388084876736800994182262062469547405871632000}\cdot t^{25}-\frac{16583198144109730963330799322654777068821323399716019726295132814280744317246437025149}{24767986692322389230965684556589778041704433986672621575251017101867589868762097120}\cdot t^{23}+\frac{3808993800338112409083036012585206694509014968501049432464417597441969356001216782096689}{31653486992788013437174144863321736337298266634967610373170799856186779852277960119360}\cdot t^{21}-\frac{13154191524745384372991468975327813851622690858835738513970694867038611678201208219027}{753654452209238415170812972936231817554720634165895485075495234671113806006618098080}\cdot t^{19}+\frac{58866060360642463773859356191755982647767822635534755132571045847793009583806186673}{29268134066378190880419921279076963788532840161782348934970688725091798291519149440}\cdot t^{17}-\frac{181612673318214385076717766013426630159789493306569626630113183308497792348587930609}{1006593275210969116152798148784693180980620025084586435546038155896350631310209103600}\cdot t^{15}+\frac{120199101386493581364561890167899866627144072861891856825876783216916067284509359147}{9797507878720099397220568648171013628211368244156641305981438050724479478086035275040}\cdot t^{13}-\frac{294542057723376517064176497696740013081948397105791654678994107220499465087253891419}{482715676640017204916905709165656479143798566183256058190854697806848392747238891820240}\cdot t^{11}+\frac{967586355951849526256164999774107824958901081354032772050113473570893137385857233312543}{45796201674191712264876678439964161489330457570937868752682766890331320716716048144769809280}\cdot t^9-\frac{11457770632802269196877957708485409746572550100559210865365449546928449147696276167861}{24170217550267848139796024732203307452702185940217208508360349192119308156044580965295177120}\cdot t^7+\frac{70873758721043439435718368808668602051390546704497717616504150164127781558130850291}{11509627404889451495140964158192051167953421876293908813504928186723480074306943316807227200}\cdot t^5-\frac{392579865323538492634320561749403243269484783346474607093171820835394142429667781}{10358664664400506345626867742372846051158079688664517932154435368051132066876248985126504480}\cdot t^3+\frac{963982297833992155603337101854639201653534852589353754642752497590116319720361}{13811552885867341794169156989830461401544106251552690576205913824068176089168331980168672640}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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