Related papers: Expressions for two generalized Furdui series

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The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…

I show that the general implicit-function problem (or parametrized fixed-point problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this…

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In this paper, we employ the theory of normal families in several complex variables to obtain some uniqueness theorems for entire functions. These results extend the related works of Li and Yi [11], and Lu et al. [18] to the setting of…

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Over a large class of function fields, we show that the solutions of some linear equations in the topological closure of a certain subgroup of the group of units in the function field are exactly the solutions that are already in the…

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Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.

We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract statement, leading to new results. This general approach does…

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The present paper presents two new approaches to Fourier series and spectral analysis of singular measures.

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For a Riemann integrable function on an interval and for a point therein,we define 'Fourier series at the point on the interval' and bring out how and when the function element becomes expressible as Fourier series.In this process,we also…

We present a systematic study of higher-order Airy-type differential equations providing the explicit form of the solutions, deriving their power series expansions and a probabilistic interpretation. Under suitable convergence hypotheses,…

We study a novel type of solutions of the general Heun's equation, based on its symmetric form. We derive the symmetry group of this equation which is a proper extension of the Mobius group. The new series solution treat simultaneously and…