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mapleintegralbessel-functions
user2863620
user2863620

Reputation: 643

Maple 18: Integral of modified bessel function

I try to calculate the following integral by Maple 18:

int(BesselK(1, x)/x^3, x);

The result is: 

(1/16)*MeijerG([[1], []], [[-1/2, -3/2], [0]], (1/4)*x^2)

However, when I calculate the derivation of the above result, I didn't get the same expression representation:

diff((1/16)*MeijerG([[1], []], [[-1/2, -3/2], [0]], (1/4)*x^2), x)

= (1/8)*MeijerG([[], []], [[-1/2, -3/2], []], (1/4)*x^2)/x

How do I tell Maple to expresse the result by modified bessel function instead of MeijerG function?

Thanks!

Upvotes: 1

Views: 485

Answers (1)

acer
acer

Reputation: 7271

restart:

igrand := BesselK(1, x)/x^3;

                                 BesselK(1, x)
                       igrand := -------------
                                       3      
                                      x       

sol := int(igrand, x);

                1         /           [[-1  -3]     ]  1  2\
         sol := -- MeijerG|[[1], []], [[--, --], [0]], - x |
                16        \           [[2   2 ]     ]  4   /

dsol := convert( diff(sol,x), StandardFunctions );

                                   /       (1/2)\
                                   |   / 2\     |
                            BesselK\1, \x /     /
                    dsol := ---------------------
                                      3          
                                     x           

simplify(dsol) assuming x>=0;

                            BesselK(1, x)
                            -------------
                                  3      
                                 x

Upvotes: 2

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