1.5k citations
- University of MichiganUS9 papers
- The University of Texas at AustinUS8 papers
- University of California, Santa CruzUS8 papers
- Carnegie Institution for ScienceUS7 papers
- Carnegie ObservatoriesUS7 papers
- University of California, BerkeleyUS7 papers
- University of California ObservatoriesUS6 papers
- Durham UniversityGB4 papers
- Ludwig-Maximilians-Universität MünchenDE4 papers
- Princeton UniversityUS4 papers
- Space Telescope Science InstituteUS4 papers
- University of ArizonaUS4 papers
49 papers
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…
Identities for squared central binomial coefficients
Khristo N. Boyadzhiev
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…
The spiral vortex. A story about tornados and bathtubs
Khristo N. Boyadzhiev
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 expl…
Exotic series with Bernoulli, harmonic, Catalan, and Stirling numbers
Khristo N. Boyadzhiev
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 Ber…
Evaluation of binomial series with harmonic numbers
Khristo N. Boyadzhiev
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.
Sums of powers and special polynomials
Khristo N. Boyadzhiev
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 fun…