BESSELK

secon secon secon

BESSELK函式

Microsoft Excel 中 BESSELK函式返回修正 Bessel 函式值，它與用純虛數參數運算時的 Bessel 函式值相等。

語法

BESSELK(X, N)

語法參數

X 必需。用來進行函式計算的數值。
N 必需。該函式的階數。如果 n 不是整數，則截尾取整。

MATLAB中的besselk函式

名稱

Modified Bessel function of second kind

語法

K = besselk(nu,Z)
K = besselk(nu,Z,1)
[K,ierr] = besselk(...)

定義

The differential equation

[1]

　(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:

[2]

(IMG[2])
where Iν(z) and I–ν(z) form a fundamental set of solutions of the modified Bessel's equation for noninteger ν:

[3]

(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.

樣例Example 1

format long
z = (0:0.2:1)';
besselk(1,z)
ans =
Inf
4.77597254322047
2.18435442473269
1.30283493976350
0.86178163447218
0.60190723019723