Rule: Q[2, 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.

• $P_1$:
  $\frac{1}{2}\cdot t^2-2\cdot t+1$
• $P_2$:
  $\frac{1}{2}\cdot t^{27}-\frac{8750463649477303436739277205122168772473173}{25630631753383395268019020534360288153774}\cdot t^{26}+\frac{31791219673694777688575307973177733869515337151}{294752265163909045582218736145143313768401}\cdot t^{25}-\frac{6176724213539220003059196446337790198399398479375}{294752265163909045582218736145143313768401}\cdot t^{24}+\frac{827526655781961403107962262121225418010256503030000}{294752265163909045582218736145143313768401}\cdot t^{23}-\frac{3532669807615808693834036539408981360275371610438000}{12815315876691697634009510267180144076887}\cdot t^{22}+\frac{263748031163115535923517131578660300202816489140532000}{12815315876691697634009510267180144076887}\cdot t^{21}-\frac{15334550140464285056086472182597777761483369197455716000}{12815315876691697634009510267180144076887}\cdot t^{20}+\frac{705415024693377933038962618635148990951861483452625800000}{12815315876691697634009510267180144076887}\cdot t^{19}-\frac{25946628363769344152171283718763361310241590573680298200000}{12815315876691697634009510267180144076887}\cdot t^{18}+\frac{768179246811207609203240282354283432373554382527299941680000}{12815315876691697634009510267180144076887}\cdot t^{17}-\frac{18372067067708421765734107259694287150127045573608628934320000}{12815315876691697634009510267180144076887}\cdot t^{16}+\frac{355337029034766646290011630541110981916895053136734149084160000}{12815315876691697634009510267180144076887}\cdot t^{15}-\frac{5551470407235213541942578227370880654135778951905697292672000000}{12815315876691697634009510267180144076887}\cdot t^{14}+\frac{69828524993991363778259216260189088810154962934220990564608000000}{12815315876691697634009510267180144076887}\cdot t^{13}-\frac{703318437358117992029665243779723456879310642198177749191116800000}{12815315876691697634009510267180144076887}\cdot t^{12}+\frac{5628627895608122067596192047278714696303399414886101775083571200000}{12815315876691697634009510267180144076887}\cdot t^{11}-\frac{35423805636356145253969117042151818081220083633372897610668185600000}{12815315876691697634009510267180144076887}\cdot t^{10}+\frac{172985601186733853181474740674407886250215544788293595639825920000000}{12815315876691697634009510267180144076887}\cdot t^9-\frac{644290922798409475215769580752076682196159734597774257203054080000000}{12815315876691697634009510267180144076887}\cdot t^8+\frac{1790281102735710169008270616918833290598360441858626163351085056000000}{12815315876691697634009510267180144076887}\cdot t^7-\frac{3606255869399106012127599033789625332159300905807606447528484864000000}{12815315876691697634009510267180144076887}\cdot t^6+\frac{5068645275178043348077061976904170855306609233578610159308357632000000}{12815315876691697634009510267180144076887}\cdot t^5-\frac{4715344214251337246047437087330915859056027109935344461599129600000000}{12815315876691697634009510267180144076887}\cdot t^4+\frac{2688087082541441141090509047545601003602786209096168554182246400000000}{12815315876691697634009510267180144076887}\cdot t^3-\frac{830341504060674488635002540706860323276741560647442763376328704000000}{12815315876691697634009510267180144076887}\cdot t^2+\frac{110703549916551995781329654112423337248101858846607526522454016000000}{12815315876691697634009510267180144076887}\cdot t-\frac{3620547355587802066230791397083136568688117383710194624299008000000}{12815315876691697634009510267180144076887}$

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.