Manuscript Topics

There are many interesting questions that interact combinatorial analysis and mathematical constants. Traditionally, combinatorial numbers (named after Bernoulli, Euler, Stirling, Catalan, and Fibonacci, etc) play a fundamental role in and have wide applications in pure mathematics, theoretical physics, and applied sciences. Working techniques in this field can be analytic, algebraic, and combinatorial. However, recent developments of computing technology make it possible to achieve higher precision in determining several mathematical constants including pi, Catalan constant, and Apery constants.

In order to promote further progress in this fast-growing interdisciplinary field, Aims Mathematics is launching a Special Issue on “Combinatorial Analysis and Mathematical Constants”, which will reflect the state of the art in the following research topics:

• Classical arithmetic functions (e.g., Riemann zeta function, Mobius function, partition function);
• Combinatorial numbers (e.g., Bernoulli/Euler numbers, Catalan numbers, Stirling numbers);
• Mathematical constants (e.g., pi, Apery’s constant, Catalan constant, harmonic numbers);
• Computations of binomial related sums and identities;
• Ramanujan and Guillera’s infinite series representations for “π”;
• Particular values of polylogarithm and polygamma functions;
• Hypergeometric series, q-series and Rogers–Ramanujan identities.

Keywords: arithmetic functions; combinatorial numbers; mathematical constants; hypergeometric series; q-series

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