Continuous Function for this please

[TheDestroyer]

Continuous Function for this please !

Hi guys,

Whats the continuous function instead of this?

f = 1/a + 1/(a+1) + 1/(a+2) + 1/(a+3) + ... + 1/(a+(n-1))

or

f = 1/a + 1/(a-1) + 1/(a-2) + 1/(a-3) + ... + 1/(a-(n-1))


(a) is any number, and i want n to not be only an integer, i want it to be generalized as we did for (n-1)! = Gamma(n)

I know riemann zeta function but it takes the sum to the infinity, i want it only to a specific REAL number

Anyone can help about this? please, as i said in my previous post, no interpolation, and only continuous function is wanted,

and Thanks

 

[shmoe]

It can be done in terms of the digamma function again. Use (6) from http://mathworld.wolfram.com/DigammaFunction.html
to derive a simple closed form. (hint: it will involve a difference of digamma functions).

 

[TheDestroyer]

HOW?? Any one can help me with this?

The Equation (6) has a some to infinity ! can you guide me?

 

[TheDestroyer]

Thanks Any way, I fixed the problem using the harmonic numbers,