Previous Page Next Page Contents

orthpoly::hermite -- the Hermite polynomials

Introduction

orthpoly::hermite(n,x) computes the value of the n-th degree Hermite polynomial at the point x.

Call(s)

orthpoly::hermite(n, x)

Parameters

n - a nonnegative integer: the degree of the polynomial.
x - an indeterminate or an arithmetical expression. An indeterminate is either an identifier (of domain type DOM_IDENT) or an indexed identifier (of type "_index").

Returns

If x is an indeterminate, then a polynomial of domain type DOM_POLY is returned. If x is an arithmetical expression, then the value of the Hermite polynomial at this point is returned as an arithmetical expression. If n is not a nonnegative integer, then orthpoly::hermite returns itself symbolically.

Details

Example 1

Polynomials of domain type DOM_POLY are returned, if identifiers or indexed identifiers are specified:

>> orthpoly::hermite(2, x)
                                    2
                            poly(4 x  - 2, [x])
>> orthpoly::hermite(3, x[1])
                                 3
                      poly(8 x[1]  - 12 x[1], [x[1]])

However, using arithmetical expressions as input the ``values'' of these polynomials are returned:

>> orthpoly::hermite(2, 6*x)
                                     2
                                144 x  - 2
>> orthpoly::hermite(3, x[1] + 2)
        2 (x[1] + 2) (2 (x[1] + 2) (2 x[1] + 4) - 2) - 8 x[1] - 16

``Arithmetical expressions'' include numbers:

>> orthpoly::hermite(2, sqrt(2)), orthpoly::hermite(3, 8 + I),
   orthpoly::hermite(1000, 0.3);
                     6, 3808 + 1516 I, 2.26821486e1433

If no integer degree is specified, then orthpoly::hermite returns itself symbolically:

>> orthpoly::hermite(n, x), orthpoly::hermite(1/2, x)
            orthpoly::hermite(n, x), orthpoly::hermite(1/2, x)

Background

Changes




Do you have questions or comments?


Copyright © SciFace Software GmbH & Co. KG 2000