A hypergeometric approach, via linear forms involving logarithms, to criteria for irrationality of Euler's constant

作     者：Sondow, Jonathan Zlobin, Sergey 

作者机构：Moscow MV Lomonosov State Univ Fac Mech & Math Moscow 119899 Russia 

出 版 物：《MATHEMATICA SLOVACA》 (斯洛伐克数学)

年 卷 期：2009年第59卷第3期

页      面：307-314页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Euler's constant irrationality hypergeometric linear forms in logarithms 

摘      要：Using an integral of a hypergeometric function, we give necessary and sufficient conditions for irrationality of Euler s constant gamma. The proof is by reduction to known irrationality criteria for gamma involving a Beukers-type double integral. We show that the hypergeometric and double integrals are equal by evaluating them. To do this, we introduce a construction of linear forms in 1, gamma, and logarithms from Nesterenko-type series of rational functions. In the Appendix, S. Zlobin gives a change-of-variables proof that the series and the double integral are equal.