Continuous Function for this please

so in summary, a continuous function for summing fractions can be derived using the digamma function and harmonic numbers.
  • #1
TheDestroyer
402
1
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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  • #2
  • #3
HOW?? Any one can help me with this?

The Equation (6) has a some to infinity ! can you guide me?
 
  • #4
Thanks Any way, I fixed the problem using the harmonic numbers,
 

What is a continuous function?

A continuous function is a type of mathematical function that has a smooth and unbroken graph. This means that there are no abrupt changes or gaps in the graph, and the function can be drawn without lifting the pencil from the paper.

Why is continuity important in mathematics?

Continuity is important in mathematics because it allows us to make predictions and draw conclusions about a function, even when we only know a limited amount of information about it. It also helps us to understand the behavior of a function and its relationship with other functions.

What are some examples of continuous functions?

Some common examples of continuous functions include linear functions, polynomial functions, exponential functions, and trigonometric functions. These functions have smooth and unbroken graphs and can be drawn without lifting the pencil from the paper.

How do you determine if a function is continuous?

A function is considered continuous if it meets three criteria: (1) it is defined at every point in its domain, (2) it has no abrupt changes or gaps in its graph, and (3) the limit of the function at every point in its domain is equal to the value of the function at that point.

What is the difference between a continuous and a discontinuous function?

A continuous function has a smooth and unbroken graph, while a discontinuous function has abrupt changes or gaps in its graph. This means that a discontinuous function cannot be drawn without lifting the pencil from the paper, and it does not meet the criteria for continuity.

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