Rule: Q[22, 23]

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.

• $P_1$:
  $\frac{263012370465}{524288}\cdot t^{22}-\frac{1412926920405}{524288}\cdot t^{20}+\frac{3273855059475}{524288}\cdot t^{18}-\frac{4281195077775}{524288}\cdot t^{16}+\frac{1735619626125}{262144}\cdot t^{14}-\frac{902522205585}{262144}\cdot t^{12}+\frac{300840735195}{262144}\cdot t^{10}-\frac{62386327575}{262144}\cdot t^8+\frac{15058768725}{524288}\cdot t^6-\frac{929553625}{524288}\cdot t^4+\frac{22309287}{524288}\cdot t^2-\frac{88179}{524288}$
• $P_2$:
  $\frac{263012370465}{524288}\cdot t^{45}-\frac{138998979507375}{24641536}\cdot t^{43}+\frac{1679770618028676225}{56749457408}\cdot t^{41}-\frac{4365110740150210577175}{45342816468992}\cdot t^{39}+\frac{1203080522311943812262954475}{5534498835388694528}\cdot t^{37}-\frac{1035105923615686180703614119015}{2861335897895955070976}\cdot t^{35}+\frac{18461282591265728300651914190486775}{40159605151546532126261248}\cdot t^{33}-\frac{2691505827100655224647056414603431064775}{5902217009517642280064489357312}\cdot t^{31}+\frac{7866502598762643999448641208597021524812289075}{21972770531923773921402940947156434944}\cdot t^{29}-\frac{3936089954196539890162810313907925572906106676525}{17556243655007095363200949816777991520256}\cdot t^{27}+\frac{49974248656540169903280925657867240969316634279108177}{444752320512294746835969661708436859182645248}\cdot t^{25}-\frac{63084721079496823527459680137362496828225382688301316325}{1400525057293216157786468464719867669566149885952}\cdot t^{23}+\frac{523171921991586924330370408109934071224406636556832665}{36377274215408211890557622460256303105614282752}\cdot t^{21}-\frac{6946602636362583544741530666887091732806589855638775}{1914593379758326941608295918960858058190225408}\cdot t^{19}+\frac{80461034042197387971327258185939008832122087139925}{112623139985783937741664465821226944599425024}\cdot t^{17}-\frac{12152558522853631455442037115957411391917413195265}{112623139985783937741664465821226944599425024}\cdot t^{15}+\frac{1374341860583611200628541515509784002963444262725}{112623139985783937741664465821226944599425024}\cdot t^{13}-\frac{787836694344923624836849332308591958151159098555}{788361979900487564191651260748588612195975168}\cdot t^{11}+\frac{44557245184108161515192221900771341901545309975}{788361979900487564191651260748588612195975168}\cdot t^9-\frac{231820271972248145657974716531862582811805825}{112623139985783937741664465821226944599425024}\cdot t^7+\frac{2432909064085431252992646371737574877896265}{56311569992891968870832232910613472299712512}\cdot t^5-\frac{265364281084252788042084008430206563641825}{619427269921811657579154562016748195296837632}\cdot t^3+\frac{393131853538300457180815028450797783701}{309713634960905828789577281008374097648418816}\cdot t$

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.