BESSELK函数

语法

语法参数

MATLAB中的besselk函数(名称 语法 定义 描述 样例 Example 1)

BESSELK函数

Microsoft Excel 中 BESSELK函数返回修正 Bessel 函数值，它与用纯虚数参数运算时的 Bessel 函数值相等。

语法

BESSELK(X, N)

语法参数

X 必需。用来进行函数计算的数值。

N 必需。该函数的阶数。如果 n 不是整数，则截尾取整。

MATLAB中的besselk函数

名称

Modified Bessel function of second kind

语法

K = besselk(nu,Z)

K = besselk(nu,Z,1)

[K,ierr] = besselk(...)

定义

The differential equation(IMG[1])

where ν is a real constant, is called the modified Bessel's equation, and its solutions are known as modified Bessel functions.

A solution Kν(z) of the second kind can be expressed as:(IMG[2])

where Iν(z) and I–ν(z) form a fundamental set of solutions of the modified Bessel's equation for noninteger ν:

(IMG[3])

and Γ(a) is the gamma function. Kν(z) is independent of Iν(z).

Iν(z) can be computed using besseli.

描述

K = besselk(nu,Z) computesthe modified Bessel function of the second kind, Kν(z),for each element of the array Z. The order nu neednot be an integer, but must be real. The argument Z canbe complex. The result is real where Z is positive.

If nu and Z are arraysof the same size, the result is also that size. If either input isa scalar, it is expanded to the other input's size. If one input isa row vector and the other is a column vector, the result is a two-dimensionaltable of function values.

K = besselk(nu,Z,1) computes besselk(nu,Z).*exp(Z).

[K,ierr] = besselk(...) alsoreturns completion flags in an array the same size as K.

ierr　Description

0　besselk successfully computed themodified Bessel function for this element.

1　Illegal arguments.

2　Overflow. Returns Inf.

3　Some loss of accuracy in argument reduction.

4　Unacceptable loss of accuracy, Z or nu toolarge.

5　No convergence. Returns NaN.

样例

Example 1

format long

z = (0:0.2:1)';

besselk(1,z)

ans =

Inf

4.77597254322047

2.18435442473269

1.30283493976350

0.86178163447218

0.60190723019723