Rule: Q[1, 2, 50]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{53}-\frac{128008855888268914275007}{9701955052549987287720}\cdot t^{51}+\frac{5364296462613634358954995}{65326497353836581070648}\cdot t^{49}-\frac{172748407299210768799924955}{538943603169151793832846}\cdot t^{47}+\frac{138040832771579462429334749455}{156832588522223172005358186}\cdot t^{45}-\frac{5727406076855738697016014385}{3168335121661074181926428}\cdot t^{43}+\frac{5378306362613267443914227477811}{1866149386658372693154666092}\cdot t^{41}-\frac{132976559276599064129406314500265}{36389913039838267516515988794}\cdot t^{39}+\frac{16368331589521401348641119957445}{4370718300331451833967507426}\cdot t^{37}-\frac{1589973202587501408535836459432545}{507003322838448412740230861416}\cdot t^{35}+\frac{3286369145518671556412073074434085}{1521009968515345238220692584248}\cdot t^{33}-\frac{587962648291561846345252651647241}{478196315858991116561808653381}\cdot t^{31}+\frac{2651016654740423961154755078071305}{4581429219681301987705070001747}\cdot t^{29}-\frac{16846552184933839587005890940907035}{74882670694101280764558730373382}\cdot t^{27}+\frac{2197193447041675678828099366383605}{30507754727226447718894297559526}\cdot t^{25}-\frac{95984007807722684090354146748025}{5084625787871074619815716259921}\cdot t^{23}+\frac{1220199969975860935511756411434574}{303690831148299638656265962069827}\cdot t^{21}-\frac{39483519400353729502267728683369515}{57498797364078064918919688818553912}\cdot t^{19}+\frac{5338203688015920249198578223270605}{57498797364078064918919688818553912}\cdot t^{17}-\frac{28131979262829389427934216610657495}{2889314567544922762175714363132334078}\cdot t^{15}+\frac{9662181712287501394480833597420215}{12520363126027998636094762240240114338}\cdot t^{13}-\frac{257909406328835822834957588601641}{5778629135089845524351428726264668156}\cdot t^{11}+\frac{172433388736213944042459168178115}{96135375611040157359664677900584933868}\cdot t^9-\frac{161670783020038095449732155252715}{3466214376198059007023465330971090115574}\cdot t^7+\frac{810553339279027439368009219805}{1155404792066019669007821776990363371858}\cdot t^5-\frac{43439138205086096238509925544699}{8693265655504731989614851050075494009859592}\cdot t^3+\frac{2302969785587148311136753817}{216250389440416218647135598260584428105960}\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.