Hp 50g Graphing Calculator Manual de usuario descargar pdf (Pagina 530)

100

101

Page 16-53

where ν is not an integer, and the function Gamma Γ(α) is defined in Chapter

If ν = n, an integer, the Bessel functions of the first kind for n = integer

are

defined by

Regardless of whether we use ν (non-integer) or n (integer) in the calculator, we

can define the Bessel functions of the first kind by using the following finite

series:

Thus, we have control over the function’s order, n, and of the number of

elements in the series, k. Once you have typed this function, you can use

function DEFINE to define function J(x,n,k). This will create the variable @@@J@@@ in

the soft-menu keys. For example, to evaluate J

(0.1) using 5 terms in the series,

calculate J(0.1,3,5), i.e., in RPN mode: .1#3#5@@@J@@@ The

result is 2.08203157E-5.

If you want to obtain an expression for J

(x) with, say, 5 terms in the series, use

J(x,0,5). The result is

‘1-0.25*x^2+0.015625*x^4-4.3403777E-4*x^6+6.782168E-6*x^8-

6.78168*x^10’.

For non-integer values ν, the solution to the Bessel equation is given by

y(x) = K

⋅J

(x)+K

⋅J

-ν

(x).

For integer values, the functions Jn(x) and J-n(x) are linearly dependent, since

(x) = (-1)

⋅J

-n

(x),

therefore, we cannot use them to obtain a general function to the equation.

Instead, we introduce the Bessel functions of the second kind

defined as

∑

∞

+⋅⋅

⋅−

⋅=

)!(!2

)1(

)(

mnm

xxJ

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Hp 50g Graphing Calculator Manual de usuario Pagina 530

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