let f(x) =∫_0 ^∞ ((cos(xcosθ))/(x^2 +θ^2 )) dθ and g(x) =∫_0 ^∞ ((sin(xcosθ))/(x^2 +θ^2 )) dθ 1) find a explicit form of f(x) and g(x) 2) find the value of ∫_0 ^∞ ((cos(2cosθ))/(4+θ^2 )) dθ and ∫_0 ^∞ ((sin(2cosθ))/(4+θ^2 )) dθ 3) let u_n =f(n^2 ) study the serie Σ u


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

$l e t f (x) = \int_{0}^{\infty} \frac{c o s (x c o s θ)}{x^{2} + θ^{2}} d θ a n d g (x) = \int_{0}^{\infty} \frac{s i n (x c o s θ)}{x^{2} + θ^{2}} d θ$ $1) f i n d a e x p l i c i t f o r m o f f (x) a n d g (x)$ $2) f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{c o s (2 c o s θ)}{4 + θ^{2}} d θ a n d \int_{0}^{\infty} \frac{s i n (2 c o s θ)}{4 + θ^{2}} d θ$ $3) l e t u_{n} = f (n^{2}) s t u d y t h e s e r i e Σ u_{n}$
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