Rule: Q[4, 10, 29]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{14}-\frac{436215}{27784}\cdot t^{12}+\frac{12954799}{583464}\cdot t^{10}-\frac{3039465}{194488}\cdot t^8+\frac{2679105}{472328}\cdot t^6-\frac{8846695}{8974232}\cdot t^4+\frac{1485}{22952}\cdot t^2-\frac{273}{390184}$
• $P_3$:
  $\frac{35}{8}\cdot t^{43}-\frac{10000227296659883079139015133943534348726535017424488730133384744027541918078231243115178574119104217955}{212297719938719737386601898842419941615401363985081421883000980082286530737677151700432936481157531104}\cdot t^{41}+\frac{35494055504501434990250788310063746847036111405655558588128034314157881622119789169885065888545495593787243}{150605329385277398700414053300680471706600823869541667442687664026499579196125281898485252845586159799747}\cdot t^{39}-\frac{117426413850339318664299475221826984424693643512062093673187589706249372352099834729984558739246391851287357883}{161448913101017371406843865138329465669476083188148667498561175836407548898246302195176191050468363305328784}\cdot t^{37}+\frac{1519224392365616821517797744656749721283006724415532087875661697474060484565862738683384398274783353615872034259}{980225543827605469255837752625571755850390505070902624098407139006760118310781120470712588520700777210924760}\cdot t^{35}-\frac{6359808410157845295075296605381751905800322338820058794541010456670397879693019897585405264268228302135833028311}{2629310870502282905768600089395651298045753354778421156405139149335780082057154064321440825679056202401068768}\cdot t^{33}+\frac{14343005491135325960153305358220141174643089699283482302496572222652916342456911995399751047805645671359343832706}{5012123846894976789121393920410460286899717332546365329397296503421330781421449935112746573950700885827037339}\cdot t^{31}-\frac{134783894271109990314566900297809824366172134854068900796970283857191039685661539146205164831794093539245416011983}{51428749037704979227506476748559505552536230020910531205989651078584089757194008029852530063146322132833948348}\cdot t^{29}+\frac{10748367072316966430928240880849717908607299986225031957752096729060326558793543976739106231581292308104295712281}{5714305448633886580834052972062167283615136668990059022887739008731565528577112003316947784794035792537105372}\cdot t^{27}-\frac{851509589190033604146400956646576800281168744459648358810798920426850029283159543641946847563198438346136651009689}{800002762808744121316767416088703419706119133658608263204283461222419174000795680464372689871165010955194752080}\cdot t^{25}+\frac{90325437173545168419508020586565239449579337022731348535677816971419426339545763817697556393661873106909445290240}{190000656167076728812732261321067062180203294243919462511017322040324553825188974110288513844401690101858753619}\cdot t^{23}-\frac{616528991222991374480407986671614952781207954451964440873321456277915942736662463401729779996104169578866343987565}{3691441319817490731218798219952160065215378288167578128785479399640591331460814354142748268976947121978970070312}\cdot t^{21}+\frac{84510839437542331224981123515230803738991632625553488442332087780177023933788202430728304487601487739225743234445}{1845720659908745365609399109976080032607689144083789064392739699820295665730407177071374134488473560989485035156}\cdot t^{19}-\frac{176582613325815867344653811933456100738553168620142511457064545138187432160808556214300750597921739795306568155845}{18262920213833901512345633298710686638433976794092228637149213871906083429332449962600965120201738392948588768912}\cdot t^{17}+\frac{16472215423381481534054657660796961160219983429069121316160111754776319472069632282596219724749046378144743970966}{10675751154410258604643219465055144027613979081840677769510018403062747298764189500196887698941457369407447111239}\cdot t^{15}-\frac{54130125484200504787556922537275781500069712633291273403487438784699219233013041799808771797864744056803947553985}{298921032323487240930010145021544032773191414291538977546280515285756924365397306005512855570360806343408519114692}\cdot t^{13}+\frac{62934972873545285050745760634673980193133004618502447273836182226184958534748908138946137902648723789476888509305}{4184894452528821373020142030301616458824679800081545685647927214000596941115562284077179977985051288807719267605688}\cdot t^{11}-\frac{4661640053804370337827575677957845059785436698162222675814938861552404640694003824375900842512808326522866522085}{5579859270038428497360189373735488611766239733442060914197236285334129254820749712102906637313401718410292356807584}\cdot t^9+\frac{709491296770422110910809608892039356450753508366887588082974087159236703672227449028335215381551244172779645}{24910086026957270077500845418462002731099284524294914795523376273813077030449775500459404630863400528617376592891}\cdot t^7-\frac{205519923224012171406123527470415496841408588431791361233334387272324811670586722024144341874509409304348081}{398561376431316321240013526695392043697588552388718636728374020381009232487196408007350474093814408457878025486256}\cdot t^5+\frac{32230449428658236859817035842922543990096112326147487381529499055581796350032515223295049603988344043265}{8664377748506876548695946232508522689078012008450405146269000443065418097547748000159792915082921922997348380136}\cdot t^3-\frac{376687886559678772043501607530195441648165943065488600939024117240351181637876943442081779407997478295}{84168240985495372187332049115797077551043545224946792849470290018349775804749552001552274032234098680545669978464}\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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