let-f-x-0-cos-xcos-x-2-2-d-and-g-x-0-sin-xcos-x-2-2-d-1-find-a-explicit-form-of-f-x-and-g-x-2-find-the-value-of-0-cos-2cos-4-

Question Number 59160 by maxmathsup by imad last updated on 05/May/19

l e t f (x) = \int_{0}^{\infty} \frac{c o s (x c o s θ)}{x^{2} + θ^{2}} d θ a n d g (x) = \int_{0}^{\infty} \frac{s i n (x c o s θ)}{x^{2} + θ^{2}} d θ

1) f i n d a e x p l i c i t f o r m o f f (x) a n d g (x)

2) f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{c o s (2 c o s θ)}{4 + θ^{2}} d θ a n d \int_{0}^{\infty} \frac{s i n (2 c o s θ)}{4 + θ^{2}} d θ

3) l e t u_{n} = f (n^{2}) s t u d y t h e s e r i e Σ u_{n}