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Volume 7, Issue 1, Article 7 |
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Approximation of $\pi(x)$ by $\Psi(x)$
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Authors: |
Mehdi Hassani, |
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Keywords:
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Primes, Harmonic series, Gamma function, Digamma function. |
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Date Received:
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07/03/05 |
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Date Accepted:
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25/08/05 |
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Subject Codes: |
11A41, 26D15, 33B15.
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Editors: |
Jozsef Sandor, |
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Abstract: |
In this paper we find some lower and upper bounds of the form  for the function  , in which  . Then, we consider  as generalization of  , such that  and  is Euler constant; this extension has been introduced for the first time by J. Sándor and it helps us to find some lower and upper bounds of the form  for the function  and using these bounds, we show that  , when  is equivalent with the Prime Number Theorem.
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