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.


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