Rule: Q[5, 6, 22]

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.

• $P_1$:
  $\frac{63}{8}\cdot t^5-\frac{35}{4}\cdot t^3+\frac{15}{8}\cdot t$
• $P_2$:
  $\frac{63}{8}\cdot t^{11}-\frac{2233}{104}\cdot t^9+\frac{71973}{3380}\cdot t^7-\frac{6901587}{746980}\cdot t^5+\frac{488523}{298792}\cdot t^3-\frac{24129}{298792}\cdot t$
• $P_3$:
  $\frac{63}{8}\cdot t^{33}-\frac{18369275210340881640397165183049821846182301424088437732768712464851}{285301340782574486962697057383837063770080913412171861992588065000}\cdot t^{31}+\frac{141120034758918375318298113925873427871159240284617725134240204256801389}{589717871397581464551894817612391210812757248022959238738679530355000}\cdot t^{29}-\frac{130736805680923371972800555760898750164516396108909530289954151835379101966}{244364342960372819373691415048134607980536284649513734552340330390853125}\cdot t^{27}+\frac{46922602484625502705881127007816082998655209823627330667227893490800606631}{58480355580260161901396236079895461738931760428943457841585720093537500}\cdot t^{25}-\frac{187390433549774162655620152790797094837681176048991252426739426088628750973}{219886136981778208749249847660406936138383419212827401484362307551701000}\cdot t^{23}+\frac{13909779682952518623135204835753949028420275218524024715449049530898949299}{21084972039348595359517108679765048670803889513558791923158029491259000}\cdot t^{21}-\frac{1783662132645191442660941519556117619937131718496732892379231646415702191531}{4727551945108231488108871724698749126975243513075789131913789612361571500}\cdot t^{19}+\frac{3779132244233634234682373668490718239143218063113439738274172612079109244037}{23637759725541157440544358623493745634876217565378945659568948061807857500}\cdot t^{17}-\frac{1803300682177929279651385323719772144970949067512875276431527236805726427379}{36151867815533534909067842600637493323928332747050152185223097035706135000}\cdot t^{15}+\frac{3017803878272817284726426810235936698409932582541363573261598159333527034743}{267523821834948158327102035244717450597069662328171126170650918064225399000}\cdot t^{13}-\frac{379705228461745299842586039649342059910233156214111415520383007768217455749}{210932244139093740219445835481411836047689541451058003326859377704485410750}\cdot t^{11}+\frac{245954478454308132757713058192720547171739862662810094962574042177151831189}{1265593464834562441316675012888471016286137248706348019961156266226912464500}\cdot t^9-\frac{392418564062729295635430326951666421000768664078362464410901518334077049631}{29530514179473123630722416967397657046676535803148120465760312878627957505000}\cdot t^7+\frac{46364923010459201596376709686577714276794823909129057750347387682886431}{89758401761316485199764185311239079169229592106833192905046543704036345000}\cdot t^5-\frac{3951442902554335341489865262834855726648098338214668559449955961903167}{421864488278187480438891670962823672095379082902116006653718755408970821500}\cdot t^3+\frac{548483152676542120640918772725219292965409445387026260034396229857861}{10968476695232874491411183445033415474479856155455016172996687640633241359000}\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.