55 citations · 212 across the 44 of their papers we have counts for
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A binomial formula for evaluating integrals
Khristo N. Boyadzhiev
In this paper we present a special formula for transforming integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Fi…
The integral formula of Poisson with principal value integrals and some special Gradshteyn and Ryzhik integrals
Khristo N. Boyadzhiev
We show how the integral formula of Poisson for holomorphic functions on the right half plane can be used to quickly evaluate certain integrals from the Table of Gradshteyn and Ryz…
Harmonic motion and Cassini ovals
Khristo N. Boyadzhiev, Irina A. Boyadzhiev
We consider a two-dimensional free harmonic oscillator where the initial position is fixed and the initial velocity can change direction. All possible orbits are ellipses and their…
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…
The values of an Euler sum at negative integers and relation to a convolution of Bernoulli numbers
Khristo N. Boyadzhiev, H. Gopalkrishna Gadiyar, R. Padma
We study a special Dirichlet series studied before by Apostol and Matsuoka and specify its values at negative integers. These values are related to a certain convolution of Bernoul…