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Modified Bessel function of the second kind

Posted 2 months ago
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The modified Bessel functions of the second kind K_m can be represented by: enter image description here

I tried to calculate this integral with Mathematica Version 12:

f[t_] := Exp[-x*Cosh[t]]*Cosh[m*t];
Integrate[f[t], {t, 0, Infinity}]

Unfortunately Mathematica does give no result by solving the integral above. Can someone explain me, how to solve this integral with Mathematica. Thank you for your help in advance. Ruediger

2 Replies
Posted 2 months ago

Check out the inbuilt function BesselK

Thank you, but I know this inbuilt function BesselK. My hope was that Methematica will give me This answer by solving the integral above. Mathematica writes only the integral as result.

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