Rule: Q[5, 25]

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.

• $P_1$:
  $\frac{-1}{120}\cdot t^5+\frac{5}{24}\cdot t^4-\frac{5}{3}\cdot t^3+5\cdot t^2-5\cdot t+1$
• $P_2$:
  $\frac{-1}{120}\cdot t^{30}+\frac{4627841573938565857578236410272540993226431763441132217004474944057802585}{697720856087799750269627896997702750475636219152408701580464258114674208}\cdot t^{29}-\frac{5143944737655869229981172716040915041140522299828402047737318345841452196415}{2093162568263399250808883690993108251426908657457226104741392774344022624}\cdot t^{28}+\frac{1032392900738969370191060698003519129669147565963349687240536407486358631719105}{1831517247230474344457773229618969719998545075275072841648718677551019796}\cdot t^{27}-\frac{54823732262807085887649876644032213474117085266013724789553397875789784647891785}{610505749076824781485924409872989906666181691758357613882906225850339932}\cdot t^{26}+\frac{6451582272125349229451081076724453509953556502051760756904824167239700689185130857}{610505749076824781485924409872989906666181691758357613882906225850339932}\cdot t^{25}-\frac{582328625475566802844299605849465034696446858774038991833131418251622002629120485625}{610505749076824781485924409872989906666181691758357613882906225850339932}\cdot t^{24}+\frac{10331498762887890093346880935257372730099968925202065688359338947483255148936930615000}{152626437269206195371481102468247476666545422939589403470726556462584983}\cdot t^{23}-\frac{586300846610985611195514788973049873914081254023589503535347781805369665977707031995000}{152626437269206195371481102468247476666545422939589403470726556462584983}\cdot t^{22}+\frac{2447288571473562337373523430937641845515196370753246902220531412885435619492038069857500}{13875130660836926851952827497113406969685947539962673042793323314780453}\cdot t^{21}-\frac{13093217404525527535459570254761942976291376016922658893550834793953959570906856716508500}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{20}+\frac{402075251183987215490295317436829345071654015389781568406089904750280299098519344762900000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{19}-\frac{10155805179582880278532087571250794509382838812102246778627579485715903649229353100468700000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{18}+\frac{211257340236894316374487018791679548290542668170209178894512552643919799445786149507850100000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{17}-\frac{3617760475089774833059166415688683845970135195013551903971847525513748782933549428123750100000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{16}+\frac{50908159209599583842967671688931409456030742701014328442219884898256019731351646617521047040000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{15}-\frac{586694975017069028896952066934715541633005045550093543848613475550794521342652149183549184000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{14}+\frac{5511021615645875735092295110683602964279971496651208649486859063891091383812057623487893392000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{13}-\frac{41926190845911628670756457359922079618837922833464085262674571274988337797086116228336889936000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{12}+\frac{256248534743986176109121954447098428879553722623714710727862491949398073682488701337721220736000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{11}-\frac{1245623180324424647032212852923514852052177332267439920063307865537807328219585233633024480332800000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^{10}+\frac{4756128944067924178020114582288946035712877472471876672389613680868902027712907419793050218880000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^9-\frac{14046193450482049397280083403783477647447797453715854355006729939907188231950753955689903866240000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^8+\frac{31469686381760312793814800994018330461287326018129172883138985300368828204486565057793734840320000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^7-\frac{52175453954838941982089202898227183686902291383387667779911561964635826719013747208486828216320000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^6+\frac{61934650669086678303464673809230150681874871698039199927515556125786886006857799973694367855820800000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^5-\frac{50254713052503168928001746692495759081712113446159798133809952275638815367792242623871179704320000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^4+\frac{25990400709695870939493483513571371209416875612087402907308738818054795550934387408470523330560000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^3-\frac{7623405692180946858377564718332492222563033644087784838479592468936751640913651207844493639680000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t^2+\frac{1012979347134088540108235161337238911037152329438434593563467069216338217917983746962655559680000000}{1982161522976703835993261071016200995669421077137524720399046187825779}\cdot t-\frac{34525359066166013663389327896199358418975949757454398692183575380452242358534211431524089856000000}{1982161522976703835993261071016200995669421077137524720399046187825779}$

Warning: This rule has negative weights!

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Laguerre type can be downloaded here packed into a single file.