prove-that-0-ln-1-x-j-0-x-dx-ln-2-Hint-1-j-0-x-n-0-1-n-x-2n-2-2n-2-n-1-Bessel-function-Hint-2-L-j-0-x-

Question Number 142362 by mnjuly1970 last updated on 30/May/21

p r o v e t h a t :

\int_{0}^{\infty} l n (\frac{1}{x}) . j_{0} (x) d x := γ + l n (2)

H i n t : (1)

j_{0} (x) = \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n} x^{2 n}}{2^{2 n} . Γ^{2} (n + 1)} (B e s s e l f u n c t i o n)

H i n t : 2

L [j_{0} (x)] = \frac{1}{\sqrt{1 + s^{2}}}

Answered by Kamel last updated on 30/May/21

Commented by mnjuly1970 last updated on 31/May/21

t h a n k s a l o t m r k a m e l