Mathematica Bessel function derivative in sum

[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

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!

 

[Orodruin]

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

 

[member 428835]

Ahh shoot,

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

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

DBesselI[1, alpha]

I receive an error. Any ideas?

 

[Orodruin]

It might help if you quote the error message.

 

[member 428835]

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?

 

[Orodruin]

Try

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

D[BesselI[L,2],{2,1}]

Edit: See also http://reference.wolfram.com/language/tutorial/ImmediateAndDelayedDefinitions.html.en

 

[member 428835]

Thanks so much! This actually makes a lot of sense!