calculate-lim-x-0-0-2-J-0-x-cos-cos-d-where-J-x-x-v-n-0-1-n-x-2n-2-2n-v-n-1-

Question Number 175080 by mnjuly1970 last updated on 18/Aug/22

c a l c u l a t e . .

{l i m}_{x \to 0^{+}} \int_{0}^{\frac{π}{2}} J_{0} (x . c o s (\emptyset)) . c o s (\emptyset) d \emptyset = ?

w h e r e :

J_{ν} (x) = x^{v} . \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n} . x^{2 n}}{2^{2 n + v} . Γ (n + ν + 1)}