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标题: 求助]怎样使用toolbox中的特殊函数? [打印本页]

作者: stheracles 时间: 2007-12-19 15:41
标题: 求助]怎样使用toolbox中的特殊函数?
要用Extended Symbolic Math Toolbox中的Hermite polynomial mhelp H的说明如下 orthopoly[H] - Hermite polynomial Calling Sequence H(n, x) orthopoly[H](n, x) Parameters n - non-negative integer x - any algebraic expression Description - The H(n,x) function computes the nth Hermite polynomial evaluated at x. - The Hermite polynomials are orthogonal on the interval (-infinity, infinity) with respect to the weight function w(x) = exp(-x^2). They satisfy: infinity / | { 0 n <> m | w(t) H(n, t) H(m, t) dt = { | { 1/2 n / { Pi 2 n! n = m -infinity - Hermite polynomials satisfy the following recurrence relation: H(0,x) = 1, H(1,x) = 2*x, H(n,x) = 2*x*H(n-1,x) - 2*(n-1)*H(n-2,x), for n > 1. Examples > with(orthopoly): > H(2,x); 2 -2 + 4 x > H(3,x); 3 8 x - 12 x > H(10,5); 3275529760 See Also HermiteH 可是我用的时候却出现错误: with(orthopoly); ??? Undefined function or variable 'orthopoly' 请问这是怎么回事?

[此贴子已经被作者于2007-12-19 15:47:39编辑过]

作者: stheracles 时间: 2007-12-19 15:47

要用Extended Symbolic Math Toolbox中的Hermite polynomial mhelp

H的说明如下

orthopoly[H] - Hermite polynomial

Calling Sequence
H(n, x)

orthopoly[H](n, x)

Parameters
n - non-negative integer

x - any algebraic expression

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

- The Hermite polynomials are orthogonal on the interval (-infinity, infinity)
with respect to the weight function w(x) = exp(-x^2). They satisfy:

infinity
/
| { 0 n <> m
| w(t) H(n, t) H(m, t) dt = {
| { 1/2 n
/ { Pi 2 n! n = m
-infinity

- Hermite polynomials satisfy the following recurrence relation:

H(0,x) = 1,
H(1,x) = 2*x,
H(n,x) = 2*x*H(n-1,x) - 2*(n-1)*H(n-2,x), for n > 1.

Examples
> with(orthopoly):
> H(2,x);

2
-2 + 4 x

> H(3,x);

3
8 x - 12 x

> H(10,5);

3275529760