## Euler’s constant, $$q$$-logarithms, and formulas of Ramanujan and Gosper.(English)Zbl 1132.11056

This paper deals with several interesting results concerning Euler’s constant $$\gamma=\lim_{n\to\infty}((\sum_{j=1}^n \frac 1j)-\log n)$$. Some tests concerning the rationality and irrationality of $$\gamma$$ are given. The problem whether $$\gamma$$ is an irrational number is not done.

### MSC:

 11Y60 Evaluation of number-theoretic constants 11J72 Irrationality; linear independence over a field 33D15 Basic hypergeometric functions in one variable, $${}_r\phi_s$$

### Keywords:

irrationality; Euler constant; hypergeometric series
Full Text:

### Online Encyclopedia of Integer Sequences:

Decimal expansion of Euler’s constant (or the Euler-Mascheroni constant), gamma.

### References:

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