Zobrazeno 1 - 10
of 153
pro vyhledávání: '"Boyadzhiev, Khristo N."'
Autor:
Boyadzhiev, Khristo N.
Publikováno v:
Mathematica Montisnigri 15(2022), 5-11
We present a summation rule using the Mellin transform to give short proofs of some important classical relations between special functions and Bernoulli and Euler polynomials. For example, the values of the Hurwitz zeta function at the negative inte
Externí odkaz:
http://arxiv.org/abs/2301.01794
Autor:
Boyadzhiev, Khristo N.
Publikováno v:
Mathematica Montisnigri, 54 (2022), 5-13
We prove a short general theorem which immediately implies some classical results of Hasse, Guillera and Sondow, Paolo Amore, and also Alzer and Richards. At the end we obtain a new representation for the Euler constant gamma. The theorem transforms
Externí odkaz:
http://arxiv.org/abs/2212.04907
Autor:
Boyadzhiev, Khristo N.
Publikováno v:
Discrete Mathematics Letters, 10 (2022), 51-55
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. Five applications are provided for evaluating challenging integrals.
Externí odkaz:
http://arxiv.org/abs/2205.08618
Autor:
Boyadzhiev, Khristo N., Kargın, Levent
Publikováno v:
Applicable Analysis and Discrete Mathematics, 2023 Apr 01. 17(1), 57-75.
Externí odkaz:
https://www.jstor.org/stable/27281395
Autor:
Boyadzhiev, Khristo N.
We prove four identities for the squared central binomial coefficients. The first three of them reflect certain transformation properties of the complete elliptic integrals of the first and the second kind, while the last one is based on properties o
Externí odkaz:
http://arxiv.org/abs/2111.08571
Autor:
Boyadzhiev, Khristo N.
Publikováno v:
The Mathematics Student, Vol 89 (3-4) (2020), 35 - 46
In this paper, we show that equiangular spirals (also known as logarithmic spirals) appear naturally in fluids going through sinks. We provide a simple mathematical model that explains the spiral forms in some natural formations. For this model we ne
Externí odkaz:
http://arxiv.org/abs/2110.15276
Autor:
Boyadzhiev, Khristo N.
We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2110.11792
Autor:
Boyadzhiev, Khristo N.
In this paper, we present a formula for generating various exotic series in the spirit of Ovidiu Furdui and Alina Sintamarian. Our new series (evaluated in closed form) involve Bernoulli, harmonic, and Catalan numbers. Also Stirling numbers of the se
Externí odkaz:
http://arxiv.org/abs/2110.00689
Autor:
Boyadzhiev, Khristo N.
This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers, derangement numbe
Externí odkaz:
http://arxiv.org/abs/2109.09167
Autor:
Boyadzhiev, Khristo N.
Publikováno v:
Discussiones Mathematicae, General Algebra ans Applications, 20 (2020), 275-283
In this paper, we discuss sums of powers of the positive integers and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show
Externí odkaz:
http://arxiv.org/abs/2108.03753