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We start from pseudo hyperbolic and trigonometric functions to introduce pseudo Laguerre and Hermite polynomials. We discuss the link with families of Bessel functions and analyze all the associated problems from a unifying point of view, employing operational tools.

$q$ -analogue of Wright function.

El-Shahed, Moustafa, Salem, Ahmed (2008)

Abstract and Applied Analysis

$q$ -extensions for the Apostol–Genocchi polynomials.

Luo, Qiuming (2009)

General Mathematics

Ramanujan's class invariants and cubic continued fraction

Bruce C. Berndt, Heng Huat Chan, Liang-Cheng Zhang (1995)

Acta Arithmetica

Rational solutions of the Sasano system of type $A_{5}^{(2)}$ .

Matsuda, Kazuhide (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Recherches sur quelques produits indéfinis et sur la constante G (Complément).

Eugène Catalan (1893)

Mémoires de l'Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique

Recursive computation of certain integrals of elliptic type.

Novario, P.G. (2005)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Regular coordinates and reduction of deformation equations for Fuchsian systems

Yoshishige Haraoka (2012)

Banach Center Publications

For a Fuchsian system $d Y / d x = (\sum_{j =}^{p} (A_{j}) / (x - t_{j})) Y$ , (F) $t ₁, t ₂, . . ., t_{p}$ being distinct points in ℂ and $A ₁, A ₂, . . ., A_{p} \in M (n \times n; ℂ)$ , the number α of accessory parameters is determined by the spectral types $s (A ₀), s (A ₁), . . ., s (A_{p})$ , where $A ₀ = - \sum_{j = 1}^{p} A_{j}$ . We call the set $z = (z ₁, z ₂, . . ., z_{α})$ of α parameters a regular coordinate if all entries of the $A_{j}$ are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues of the matrices...

Relations between holomorphic quadratic differentials II

Hershel M. Farkas (1981)

Compositio Mathematica

Remarques sur la décomposition en éléments simples des fonctions doublement périodiques

Hermite (1888)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Remarques sur la théorie des nombres et sur les fractions continues.

Eugène Catalan (1894)

Mémoires de l'Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique

Renewal Processes of Mittag-Leffler and Wright Type

Mainardi, Francesco, Gorenflo, Rudolf, Vivoli, Alessandro (2005)

Fractional Calculus and Applied Analysis

2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore consider corresponding...

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Příspěvek ku transformaci jedenáctého řádu funkcí elliptických

Probabilistic derivation of a bilinear summation formula for the Meixner- Pollaczek polynomials.

Properties of the L function

Properties of the van der Pol numbers and polynomials.

Propriétés d'indépendance algébrique de nombres liés aux fonctions de Weierstrass

Pseudo Laguerre and pseudo Hermite polynomials