I was trying to Generalize the Harmonic Function, define H(n)=1+1/2+1/3+..+1/n

for integral values of n. Now how can H(x) be defined in such as way such as it will be countinous and H(x)=H(n) for integral values of x. This is anagolus with the Gamma function as a generalization for the factoril.

Thus given:

H(x) is countinous for x>1 or x=1.

H(1)=1

H(x+1)=H(x)+1/(x+1)

Find a possible H.