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The Euler Series Transformation and the Binomial Identities of Ljunggren, Munarini and Simons
Khristo N. Boyadzhiev
It is shown that the curious identity of Simons follows immediately from Euler's series transformation formula and also from an identity due to Ljunggren. The relation of Simons' i…
Series Transformation Formulas of Euler Type, Hadamard Product of Functions, and Harmonic Number Identities
Khristo N. Boyadzhiev
The integral representation of the Hadamard product of two functions is used to prove several Euler-type series transformation formulas. As applications we obtain three binomial id…
Evaluation of some simple Euler-type series
Khristo N. Boyadzhiev
Five series are evaluated in terms of zeta values. Three of the series involve harmonic numbers and one involves Stirling numbers of the first kind. The evaluation of these series…
Power sum identities with generalized Stirling numbers
Khristo N. Boyadzhiev
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first k…
Exponential Polynomials, Stirling Numbers,and Evaluation of Some Gamma Integrals
Khristo N. Boyadzhiev
This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and seve…
Derivative Polynomials for tanh, tan, sech and sec in Explicit Form
Khristo N. Boyadzhiev
The derivative polynomials for the hyperbolic and trigonometric tangent, cotangent and secant are found in explicit form, where the coefficients are given in terms of Stirling numb…