55 citations · 212 across the 44 of their papers we have counts for
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Series with Hermite Polynomials and Applications
Khristo N. Boyadzhiev, Ayhan Dil
We obtain a series transformation formula involving the classical Hermite polynomials. We then provide a number of applications using appropriate binomial transformations. Several…
Equiangular surfaces, self-similar surfaces and the geometry of sea shells
Khristo N. Boyadzhiev
We investigate three-dimensional surfaces where the normal vector forms a constant angle with the radius vector. These surfaces naturally extend equiangular (logarithmic) spirals i…
Power series with skew-harmonic numbers, dilogarithms, and double integrals
Khristo N. Boyadzhiev
The skew-harmonic numbers are the partial sums of the alternating harmonic series, i.e. the expansion of log(2). We evaluate in closed form various power series and numerical serie…
Binomial transform of products
Khristo N. Boyadzhiev
Given two infinite sequences with known binomial transforms, we compute the binomial transform of the product sequence. Various identities are obtained and numerous examples are gi…
The formula of Melzak for arbitrary polynomials
Khristo N. Boyadzhiev
We extend the well-known Melzak binomial transform formula to polynomials of any degree and show some applications.