Hermite polynomial - Maple Help

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orthopoly[H] - Hermite polynomial

Calling Sequence

H(n, x)

Parameters

n

-

non-negative integer

x

-

algebraic expression

Description

• 

The H(n, x) function computes the nth Hermite polynomial evaluated at x.

• 

The Hermite polynomials are orthogonal on the interval (,) with respect to the weight function wx=ⅇx2. They satisfy:

wtHn,tHm,tⅆt=0nmπ2nn!n=m

• 

Hermite polynomials satisfy the following recurrence relation:

H0,x=1,

H1,x=2x,

Hn,x=2xHn1,x2n1Hn2,x,for n>1.

Examples

withorthopoly:

H2,x

4x22

(1)

H3,x

8x312x

(2)

H10,5

3275529760

(3)

See Also

HermiteH


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