## The $$q$$-gamma function for $$q>1$$.(English)Zbl 0437.33002

### MSC:

 33B15 Gamma, beta and polygamma functions 26A51 Convexity of real functions in one variable, generalizations 26D15 Inequalities for sums, series and integrals

### Keywords:

q-gamma function; inequalities; Bohr-Mollerup theorem

Zbl 0398.33001
Full Text:

### References:

 [1] Artin, E.,The gamma function. Holt, Rinehart and Winston, New York, 1964. · Zbl 0144.06802 [2] Askey, R.,The q-gamma and q-beta functions. Applicable Anal. to appear. · Zbl 0398.33001 [3] Bohr, H. andMollerup, J.,Laerebog Matematisk Analyse, Vol. III, Copenhagen, 1922. [4] Jackson, F. H.,On q-definite integrals. Quart. J. Pure Appl. Math.41 (1910), 193–203. · JFM 41.0317.04 [5] John, F.,Special solutions of certain difference equations. Acta Math.71 (1939), 175–189. · Zbl 0021.39603
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