Problem with symbolic math integration of besselk times exponent
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According to Mathematica and the G&R book, the integral
where K0 is the modified bessel function of the second kind, has a closed form solution that can be expressed using the Meijer G function or the hypergeometric function. However, Matlab's symbolic integrations outputs,
syms x
>> I = int(besselk(0,x/a) * exp(-x/a),x)
I =
x*exp(-x/a)*(besselk(0, x/a) - besselk(1, x/a))
which is obviously the wrong answer. Matlab itself confirms that, by the way, since,
diff(I,x)
ans =
exp(-x/a)*(besselk(0, x/a) - besselk(1, x/a)) + x*exp(-x/a)*(besselk(0, x/a)/a - besselk(1, x/a)/a + besselk(1, x/a)/x) - (x*exp(-x/a)*(besselk(0, x/a) - besselk(1, x/a)))/a
What am I doing wrong?
Thanks!
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Walter Roberson
2019-10-3
MATLAB is correct, that is one of the ways of expressing the integral.
convert(BesselK(v, z), MeijerG);
1 / [[1 1 ] ] 1 2\
- MeijerG|[[], []], [[- v, - - v], []], - z |
2 \ [[2 2 ] ] 4 /
What am I doing wrong?
You failed to simplify() the differentiation.
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