Answer to Question #163437 in Calculus for Amedeka Israel Yao

Question

1). show that fourier series of f(t) = a^2/t(t/2- τ) is given by the f(t) = a^2/t _∑_(-∞)^∞▒〖(a^2/π^(2n^2 ) x^i2πnfτ)〗Does the function holds for only odd values of n

Answer 1

 and cosine terms) of the form 

∑

∞

=













= + +

1

cos sin

2

( )

n

n n

L

n x

b

L

n x

a

a

f x

π π

Where the coefficients are given by the Euler-Fourier formulas: