- #1

Math Monster

- 11

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**Homework Statement**

Show that the formula:

∫_0^∞ (s^a-1)/(s-1) ds = -pi cot (a pi)

may be calculated by considering an analytical branch of function:

f(z) = z^(a-1) / (z-1)

and integrating along a contour consisting of:

a) a circle radius R, centred at (0,0)

b) with a branch cut running from (0,0) to R above and below the x-axis

c) circular contours around singularity (0,0) and (1,0)

when R→∞

I have attempted to substitute s=Re^i alpha z, and I believe the integral around (a) → 0 as R → infinity but i can't really make sense of it all!

Please help and thanks in advance!