Rule: Q[2, 3, 4, 18]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^9-\frac{142}{3}\cdot t^7+\frac{1399}{9}\cdot t^5-\frac{2965}{18}\cdot t^3+\frac{295}{6}\cdot t$
• $P_4$:
  $4\cdot t^{27}-\frac{8054880965040595537504108712022329}{1308210241253142446361111433731}\cdot t^{25}+\frac{38318532686490862474726678493408987389}{54944830132631982747166680216702}\cdot t^{23}-\frac{3709235259758805845518111914465376906699}{109889660265263965494333360433404}\cdot t^{21}+\frac{65453924789021995893651495904258813923893}{73259773510175976996222240288936}\cdot t^{19}-\frac{43255743556930569928321216757676028801511}{3052490562923999041509260012039}\cdot t^{17}+\frac{6823477816157005987362812950159827283444729}{48839849006783984664148160192624}\cdot t^{15}-\frac{12043632963166837691018952653624243452039725}{13954242573366852761185188626464}\cdot t^{13}+\frac{46042208177338761495372292691268263221146285}{13954242573366852761185188626464}\cdot t^{11}-\frac{844353751622751312357970658347724980970739555}{111633940586934822089481509011712}\cdot t^9+\frac{2195390217545643743067297557248776952554001455}{223267881173869644178963018023424}\cdot t^7-\frac{2933303286161246373455525132291856194622316065}{446535762347739288357926036046848}\cdot t^5+\frac{1644110385427518271189164617717505558924272025}{893071524695478576715852072093696}\cdot t^3-\frac{111889442686943409393747161516766198799180725}{893071524695478576715852072093696}\cdot t$

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.