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Dr. Khristo Boyadzhiev articles published

Dr. Khristo Boyadzhiev, professor of mathematics, has recently published the article, “Series Transformation Formulas of Euler Type, Hadamard Product of Functions, and Harmonic Number Identities,” in volume 42 of the Indian Journal of Pure and Applied Mathematics.

In the article Boyadzhiev uses a theorem originally proven by the French mathematican Jacques Hadamard concerning the multiplication of series to establish several Euler-type series transformation formulas. As applications he obtains a number of binomial identities involving harmonic numbers and an identity for the Laguerre polynomials. He also evaluates in a closed form certain power series with harmonic numbers.

Boyadzhiev was also recently recognized for the solution of two problems:  Problem 938 in The College Mathematics Journal and Problem 11506 in The American Mathematical Monthly. The first problem deals with a special integrals sum involving finite geometric series and some Lebesgue theory. It provides a nice illustration of some ideas and techniques from ergodic theory. The second problem was solved by only 10 individuals in the world and one problem solving group. It is based on an interesting property of the integral Hilbert transform. The technique used to solve this difficult problem is important in advanced calculus.