Rule: Q[1, 56]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{57}-1596\cdot t^{55}+592515\cdot t^{53}-136080945\cdot t^{51}+\frac{173503204875}{8}\cdot t^{49}-\frac{5100994223325}{2}\cdot t^{47}+\frac{1838058251804775}{8}\cdot t^{45}-\frac{129976976377623375}{8}\cdot t^{43}+\frac{117369209668993907625}{128}\cdot t^{41}-\frac{2673409775793750118125}{64}\cdot t^{39}+\frac{396199328772633767506125}{256}\cdot t^{37}-\frac{11994034225571549507230875}{256}\cdot t^{35}+\frac{2378816788071690652267456875}{2048}\cdot t^{33}-\frac{6038534923566599348063544375}{256}\cdot t^{31}+\frac{401131248494066956692792590625}{1024}\cdot t^{29}-\frac{5428642896286372813909126393125}{1024}\cdot t^{27}+\frac{1905453656596516857682103363986875}{32768}\cdot t^{25}-\frac{8406413190866986136832808958765625}{16384}\cdot t^{23}+\frac{236313615254371943624300074063078125}{65536}\cdot t^{21}-\frac{1305943663247844951607974093506484375}{65536}\cdot t^{19}+\frac{44663273283076297344992713997921765625}{524288}\cdot t^{17}-\frac{36155983133918907374517911331650953125}{131072}\cdot t^{15}+\frac{345125293551044115847670971802122734375}{524288}\cdot t^{13}-\frac{585212454282205239915615995664468984375}{524288}\cdot t^{11}+\frac{10728894995173762731786293253848598046875}{8388608}\cdot t^9-\frac{3862402198262554583443065571385495296875}{4194304}\cdot t^7+\frac{6239265089501049711715721307622723171875}{16777216}\cdot t^5-\frac{1155419461018712909576985427337541328125}{16777216}\cdot t^3+\frac{495179769008019818390136611716089140625}{134217728}\cdot t$

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.