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We prove that if f and g are holomorphic functions on an open connected domain, with the same moduli on two intersecting segments, then f = g up to the multiplication of a unimodular constant, provided the segments make an angle that is an irrational multiple of $pi$. We also prove that if f and g are functions in the Nevanlinna class, and if |f | = |g| on the unit circle and on a circle inside the unit disc, then f = g up to the multiplication of a unimodular constant.
In this note, we aim to provide generalizations of (i) Knuths old sum (or Reed Dawson identity) and (ii) Riordans identity using a hypergeometric series approach.
We study some properties of tau-functions of an isomonodromic deformation leading to the fifth Painleve equation. In particular, here is given an elementary proof of Miwas formula for the logarithmic differential of a tau-function.
Let $mathsf M$ and $mathsf M _{mathsf S}$ respectively denote the Hardy-Littlewood maximal operator with respect to cubes and the strong maximal operator on $mathbb{R}^n$, and let $w$ be a nonnegative locally integrable function on $mathbb{R}^n$. We
In the article [Petojevic 2006], A. Petojevi c verified useful properties of the $K_{i}(z)$ functions which generalize Kurepas [Kurepa 1971] left factorial function. In this note, we present simplified proofs of two of these results and we answer the
In the present investigation our main aim is to give lower bounds for the ratio of some normalized $q$-Bessel functions and their sequences of partial sums. Especially, we consider Jacksons second and third $q$-Bessel functions and we apply one normalization for each of them.