Rule: Q[2, 10, 26]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{12}-\frac{3091}{728}\cdot t^{10}+\frac{61875}{13832}\cdot t^8-\frac{36135}{16796}\cdot t^6+\frac{7755}{16796}\cdot t^4-\frac{15543}{436696}\cdot t^2+\frac{189}{436696}$
• $P_3$:
  $\frac{3}{2}\cdot t^{38}-\frac{575210109029206497010844676284625063467551624539441839453751030353}{40391260573508167001482603691765785770209803874970556280645560824}\cdot t^{36}+\frac{2497460484451082502644788017102394339017930700954440191591538104813875}{40125832289739399046901432296077039178005568020935035482229889995728}\cdot t^{34}-\frac{1790621647257194385707363159303349196296907127125049880636496349422544705}{10784932034319956254939396080467817530177274338071316759057122655518448}\cdot t^{32}+\frac{1184200178266855446225153953148582727219739296187041497243306256904959698985}{3918974677971014104138603050739993195028167062596664727322381944949016042}\cdot t^{30}-\frac{30362956923765708687881556540052490127322300632504952871326394853710664104647}{76420006220434775030702759489429867303049257720634962182786447926505812819}\cdot t^{28}+\frac{233941298412817313717450518598963912792899930750393383914285857792900546435861}{600038567360450826166999444879967846972090468028689332694471368904416011764}\cdot t^{26}-\frac{4305677390934750906284384742534696073685062384507915841542801378532809226625}{14805015450112719948968055969462196514550853347587400080995665125362949492}\cdot t^{24}+\frac{9598824569930195619618099934874662763163852717892034619542459223191785853545675}{57672937685914100561205062029039986522432849215526717015518613495851369746086}\cdot t^{22}-\frac{402248973134816294390007709175285789209904254584421421534874654992306641505725}{5492660731991819101067148764670474906898366591954925430049391761509654261532}\cdot t^{20}+\frac{14268416436448579736982822589218334902613702775306533492080819383002685810265}{578174813893875694849173554175839463884038588626834255794672817001016238056}\cdot t^{18}-\frac{9220957858734247896379278182486979435050634572772414594399144517939459485755}{1462442176319803228147909578209476291000803488879639588186525360649629308024}\cdot t^{16}+\frac{846086338389879804244825541006909323454139966096645777146183785893789857487875}{704531518442065205160255439302415203189637080767766371608858592492958919140562}\cdot t^{14}-\frac{196714428805610974187298975329397205997312465050217406093707528592592548400}{1183423603206156559619689987630036735480913349553918877282517232630950032151}\cdot t^{12}+\frac{204266024529137052917794773466995584383026363361353912742396459762194640196425}{12681567331957173692884597907443473657413467453819794688959454664873260544530116}\cdot t^{10}-\frac{10197699854443246319983128292824040681793816123116568531876274153040271874755}{9863441258188912872243576150233812844654919130748729202524020294901424867967868}\cdot t^8+\frac{14215072690660761628650011774629061419635985758062865291188537010957648330}{352265759221032602580127719651207601594818540383883185804429296246479459570281}\cdot t^6-\frac{1001281230639196939799510812717937581748229030268898655769691197954096375}{1207768317329254637417580753089854634039377852744742351329471872845072432812392}\cdot t^4+\frac{492937411052187772488492712172398199039266528104147452667819505179792475}{73271277917974781336666565687451181131722256399847702647321293619267727590618448}\cdot t^2-\frac{292541143970320132990097609163440001891010869879198559958033757375}{32406580237936656937933023302720557776082377885823840180150948084594306762768}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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