منابع مشابه
Formulas of Ramanujan and Gosper
Abstract. The aim of the paper is to relate computational and arithmetic questions about Euler’s constant γ with properties of the values of the q-logarithm function, with natural choice of q. By these means, we generalize a classical formula for γ due to Ramanujan, together with Vacca’s and Gosper’s series for γ, as well as deduce irrationality criteria and tests and new asymptotic formulas fo...
متن کاملEULER’S CONSTANT, q-LOGARITHMS, AND FORMULAS OF RAMANUJAN AND GOSPER
The aim of the paper is to relate computational and arithmetic questions about Euler’s constant γ with properties of the values of the q-logarithm function, with natural choice of q. By these means, we generalize a classical formula for γ due to Ramanujan, together with Vacca’s and Gosper’s series for γ, as well as deduce irrationality criteria and tests and new asymptotic formulas for computin...
متن کاملRamanujan-like formulas for 1/π2 a la Guillera and Zudilin and Calabi-Yau differential equations
Using the PSLQ-algorithm J.Guillera found some formulas for 1 π2 . He proved three of them using WZ-pairs. Then W. Zudilin showed how to produce formulas for 1 π2 by squaring formulas for 1 π . The success of this depends on facts related to CalabiYau differential equations of string theory. Here some examples of this is worked out. Also some formulas containing harmonic numbers are found by di...
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In their last published paper [9], [16, pp. 310–321], G. H. Hardy and S. Ramanujan derived infinite series representations for the coefficients of certain modular forms of negative weight which are not analytic in the upper half-plane. In particular, they examined in detail the coefficients of the reciprocal of the Eisenstein series E6(τ). While confined to the sanitarium, Matlock House, in 191...
متن کاملThe power of Mathematica for investigation of BBP, Adamchik-Wagon, Chudnovsky’s, and Ramanujan formulas of Pi
The BBP, BBP-type, Adamchik-Wagon, Chudnovsky's, and Ramanu-jan formulas of Pi are investigating by Mathematica. We point out errors of two BBP-like formulas.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2013
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2013.04.010