Rule: Q[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.

• $P_1$:
  $\frac{209863810776486386280915}{549755813888}\cdot t^{42}-\frac{2177020976850057573347805}{549755813888}\cdot t^{40}+\frac{5240976425750138602503975}{274877906944}\cdot t^{38}-\frac{15546018680600622099410525}{274877906944}\cdot t^{36}+\frac{63597349147911635861224875}{549755813888}\cdot t^{34}-\frac{95141634325275807248392413}{549755813888}\cdot t^{32}+\frac{13467537278920319747489337}{68719476736}\cdot t^{30}-\frac{11787482326620400583818635}{68719476736}\cdot t^{28}+\frac{32287451590308053773068435}{274877906944}\cdot t^{26}-\frac{17402026147346795151322125}{274877906944}\cdot t^{24}+\frac{3694584012821319585973005}{137438953472}\cdot t^{22}-\frac{1231528004273773195324335}{137438953472}\cdot t^{20}+\frac{639317816426275702490775}{274877906944}\cdot t^{18}-\frac{127530151125450042348225}{274877906944}\cdot t^{16}+\frac{4794366583663535426625}{68719476736}\cdot t^{14}-\frac{528833162561674816755}{68719476736}\cdot t^{12}+\frac{329273478576137150055}{549755813888}\cdot t^{10}-\frac{17090318957238952425}{549755813888}\cdot t^8+\frac{271274904083157975}{274877906944}\cdot t^6-\frac{4556689318306125}{274877906944}\cdot t^4+\frac{60755857577415}{549755813888}\cdot t^2-\frac{67282234305}{549755813888}$

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.