Rule: Q[2, 44]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{46}-\frac{652618759244694300136298254}{328554527712538859293821}\cdot t^{44}+\frac{147843161308428442702882534487}{328554527712538859293821}\cdot t^{42}-\frac{1931673809424984673454917269341}{31290907401194177075602}\cdot t^{40}+\frac{359350760788782222844235780635135}{62581814802388354151204}\cdot t^{38}-\frac{48088733100800756271685634741077765}{125163629604776708302408}\cdot t^{36}+\frac{4793538669643366861204530466109832645}{250327259209553416604816}\cdot t^{34}-\frac{363669080576741295726834409793149497195}{500654518419106833209632}\cdot t^{32}+\frac{10638278566648275608891163502015826036205}{500654518419106833209632}\cdot t^{30}-\frac{483469422378515934095438914521460853535975}{1001309036838213666419264}\cdot t^{28}+\frac{17114153390549405080171026219639526359173175}{2002618073676427332838528}\cdot t^{26}-\frac{471343440903367731977154543442685958888464625}{4005236147352854665677056}\cdot t^{24}+\frac{10051953136613388127832888908199421423885783375}{8010472294705709331354112}\cdot t^{22}-\frac{164596511353522504235705583559780169096986105125}{16020944589411418662708224}\cdot t^{20}+\frac{2043552433628788824141758728595832027718485313125}{32041889178822837325416448}\cdot t^{18}-\frac{18903609717232533926149205139151118529031452406875}{64083778357645674650832896}\cdot t^{16}+\frac{254444769171771327690787068699371255630015319298125}{256335113430582698603331584}\cdot t^{14}-\frac{1206207101484704284148798911079075984266756210404375}{512670226861165397206663168}\cdot t^{12}+\frac{3851416510085025553983783077951054730002382119094375}{1025340453722330794413326336}\cdot t^{10}-\frac{7768595482246110156525718773028809910326295579040625}{2050680907444661588826652672}\cdot t^8+\frac{8981581027375602654009994990221907328379413226421875}{4101361814889323177653305344}\cdot t^6-\frac{5062234556861893634917131213002486273072866172990625}{8202723629778646355306610688}\cdot t^4+\frac{1011560207500850556576228390815270305758041309990625}{16405447259557292710613221376}\cdot t^2-\frac{27935260452304471699310794304065169594696878659375}{32810894519114585421226442752}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.