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HermiteH

Hermite function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

HermiteH(n, x)

Parameters

n

-

algebraic expression

x

-

algebraic expression

Description

• 

For a non-negative integer n, the HermiteH(n, x) function computes the nth Hermite polynomial.

• 

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

wtHermiteHn,tHermiteHm,tⅆt={0nmπ2nn!n=m

• 

Hermite polynomials satisfy the following recurrence relation:

HermiteHn,x=2xHermiteHn1,x2n1HermiteHn2,x,for n >= 2

  

where HermiteH(0,x) = 1 and HermiteH(1,x) = 2*x.

• 

For n different from a non-negative integer, the analytic extension of the Hermite polynomial is given by:

HermiteHn,x=2nπKummerM12n,12,x2Γ1212n2xKummerM1212n,32,x2Γ12n

Examples

HermiteH3,x

HermiteH3,x

(1)

simplify,'HermiteH'

8x312x

(2)

HermiteH3.2,2.1

59.58210770

(3)

See Also

ChebyshevT

ChebyshevU

expand

GegenbauerC

JacobiP

KummerM

LaguerreL

LegendreP

orthopoly[H]

simplify

 


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