Bessel function derivative in sum

• Mathematica
• member 428835
In summary, the conversation was about an issue with using the modified Bessel function and its derivative in a sum. The error was caused by a typo and a delayed definition. Once the delayed definition was changed to an immediate one, the issue was resolved.
member 428835
Hi PF!

I'm trying to put the first derivative of the modified Bessel function of the first kind evaluated at some point say ##\alpha## in a sum where the ##ith## function is part of the index. What I have so far is
Code:
n=3;
alpha = 2;
DBesselI[L_, x_] := D[BesselI[L, x], {x, 1}]
Sum[BesselI[L, alpha], {L, 1, n}]
But I don't think this is working. Any help would be awesome!

You are using the modified Bessel function, not its derivative that you defined in the previous line, in the sum ...

Ahh shoot,
Orodruin said:
You are using the modified Bessel function, not its derivative that you defined in the previous line, in the sum ...
Shoot, this is a typo on my part copying into PF. Instead if I use
Code:
n=3;
alpha = 2;
DBesselI[L_, x_] := D[BesselI[L, x], {x, 1}]
Sum[DBesselI[L, alpha], {L, 1, n}]
I still get an error. In fact, even if I simply try evaluating
Code:
DBesselI[1, alpha]
I receive an error. Any ideas?

It might help if you quote the error message.

Orodruin said:
It might help if you quote the error message.
It reads "2 is not a valid variable." and then iterates "##\partial_{\{2,1\}}BesselI[1,3]##". Any ideas?

Try
Code:
DBesselI[L_, x_] = D[BesselI[L, x], {x, 1}]
instead. When you use := it is a delayed definition. The RHS will be evaluated only once the function is called. Since you were calling it with x = 2, it thinks you want to differentiate with respect to 2, i.e., it executes
Code:
D[BesselI[L,2],{2,1}]

Last edited:
member 428835
Thanks so much! This actually makes a lot of sense!

1. What is a Bessel function derivative in sum?

A Bessel function derivative in sum is a mathematical expression that involves the derivative of a Bessel function, which is a special type of mathematical function that appears in many areas of science and engineering. The sum refers to the summation of multiple terms in the expression.

2. What is the purpose of using a Bessel function derivative in sum?

The Bessel function derivative in sum is useful for solving differential equations that involve Bessel functions. It can also be used for approximating other functions and for studying the behavior of physical systems.

3. How do you calculate the Bessel function derivative in sum?

The Bessel function derivative in sum can be calculated using a series expansion, which involves summing an infinite number of terms. This can be done manually or using computer software such as Mathematica or MATLAB.

4. What are some real-world applications of Bessel function derivative in sum?

Bessel function derivative in sum has many applications in physics and engineering. It is used in the study of wave phenomena, such as sound and electromagnetic waves, as well as in solving problems related to heat transfer and fluid dynamics.

5. Are there any limitations or special considerations when using Bessel function derivative in sum?

One limitation of using Bessel function derivative in sum is that the series expansion may not converge for certain values of the input parameters. Additionally, caution must be taken when dealing with complex numbers, as the Bessel function can have complex values. Special techniques, such as the use of contour integration, may be needed in these cases.

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