Anonymous

# What is the Fourier transform of k^x?

Update:

I'm sorry. I meant f(x)=k^(-x), k is a nonnegative integer

I want to evaluate int(f(x)*exp(-2*i*Pi*s*x),x,-infinity,infinity).

This means you integrate [k^(-x)*exp(-2*i*Pi*s*x)] with respect to x from minus infinity to positive infinity. My eternal gratitude I offer to those who answered.

Relevance
• Helmut
Lv 7

k^x = e^xln(k) and has no Fourier transform

k^-x = e^-xln(k) has the transform

(√(2/π))[(ln(k))/(((ln(k))^2 + ω^2)] , k > 1, x > 0

• Sean H
Lv 5