Continuous Function for this please

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    Continuous Function
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Discussion Overview

The discussion revolves around finding a continuous function that generalizes a series of terms involving reciprocals, specifically for non-integer values of n. Participants explore different mathematical functions and approaches to achieve this goal without using interpolation.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks a continuous function to represent the sum of reciprocals for a generalized n, specifically avoiding interpolation methods.
  • Another participant suggests that the digamma function could be used to derive a closed form for the problem, hinting at a relationship involving differences of digamma functions.
  • A later reply questions the applicability of the digamma function, noting that it is associated with sums to infinity and asks for further guidance.
  • One participant claims to have resolved the issue using harmonic numbers, indicating a potential alternative approach.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the appropriate mathematical tools to use, and it remains unresolved whether the digamma function is suitable for the original request.

Contextual Notes

Participants express uncertainty about the applicability of certain functions and the implications of using sums to infinity versus specific real numbers.

TheDestroyer
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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
 
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HOW?? Any one can help me with this?

The Equation (6) has a some to infinity ! can you guide me?
 
Thanks Any way, I fixed the problem using the harmonic numbers,
 

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