Rule: Q[5, 42]

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.

• $P_1$:
  $32\cdot t^5-160\cdot t^3+120\cdot t$
• $P_2$:
  $32\cdot t^{47}-\frac{96673312451812223386203218778416}{6062989709009127413615092763}\cdot t^{45}+\frac{417791019515624629302962557866556440}{115196804471173420858686762497}\cdot t^{43}-\frac{57593968464063468574240185371528409660}{115196804471173420858686762497}\cdot t^{41}+\frac{414474526937864519673505297514294278950}{8861292651628724681437443269}\cdot t^{39}-\frac{1469792988804031235541802727880437157345}{466383823769932877970391751}\cdot t^{37}+\frac{147745609997502383846464291221740937595515}{932767647539865755940783502}\cdot t^{35}-\frac{11323851931734135557003805728872894783589775}{1865535295079731511881567004}\cdot t^{33}+\frac{335409429141776005417497744866680104834281475}{1865535295079731511881567004}\cdot t^{31}-\frac{15478991415043210444586521556461364812281940875}{3731070590159463023763134008}\cdot t^{29}+\frac{558480619033498695720799461100744730018242071225}{7462141180318926047526268016}\cdot t^{27}-\frac{15752812414778707395811676122703938072271219981325}{14924282360637852095052536032}\cdot t^{25}+\frac{346244620237813618703200371824213820612832693220625}{29848564721275704190105072064}\cdot t^{23}-\frac{5892723240500802924927144540225297696901947771830625}{59697129442551408380210144128}\cdot t^{21}+\frac{76907397856737809717236622688820071509020863840946875}{119394258885102816760420288256}\cdot t^{19}-\frac{759541446273408159992371784224450459495735936934649375}{238788517770205633520840576512}\cdot t^{17}+\frac{11152799106172287692772797742601924263831764719252231875}{955154071080822534083362306048}\cdot t^{15}-\frac{59457406625701624494136965852498445155553264857578446875}{1910308142161645068166724612096}\cdot t^{13}+\frac{223033480663511672359435075630979650790966480231473715625}{3820616284323290136333449224192}\cdot t^{11}-\frac{563476573862874596760432912434651623236225866268436078125}{7641232568646580272666898448384}\cdot t^9+\frac{898893692825998097097524089690322801623793677594473778125}{15282465137293160545333796896768}\cdot t^7-\frac{816029399917821761606448883369480451411849857192597978125}{30564930274586321090667593793536}\cdot t^5+\frac{348029524649384212588888010645384486904261408217071609375}{61129860549172642181335187587072}\cdot t^3-\frac{44335989471845965337836263429333145906504114639289671875}{122259721098345284362670375174144}\cdot t$

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.