A112734 Triangle of coefficients (read in increasing degree) of the polynomials whose roots are weights in Legendre-Gauss quadrature.

-2, 1, -1, 1, -5, 9, 49, -216, 216, 5103, -32200, 45000, -58564, 629325, -2025000, 2025000, -1976763932, 27510743799, -113071253400, 142943535000, 4373849390625, -88878097916608, 606530263046400, -1707698764800000, 1707698764800000

Offset

1,1

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Legendre-Gauss Quadrature

Example

Polynomials are -2 + x, -1 + x, -5 + 9*x, 49 - 216*x + 216*x^2, 5103 - 32200*x + 45000*x^2, ... hence we get
-2, 1; -1, 1; -5, 9; 49, -216, 216; 5103, -32200, 45000; ...

Crossrefs

Sequence in context: A090628 A054387 A199958 * A351699 A260685 A351429

Adjacent sequences: A112731 A112732 A112733 * A112735 A112736 A112737

Keyword

sign,tabf

Author

Eric W. Weisstein, Sep 16 2005

Status

approved