A characterization of the Rogers -Hermite polynomials.
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Al-Salam, Waleed A. (1995)
International Journal of Mathematics and Mathematical Sciences
Fang, Jian-Ping (2007)
The Electronic Journal of Combinatorics [electronic only]
Bennewitz, Christer, Saitō, Yoshimi (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Peter M. Gruber (1996)
Manuscripta mathematica
Shabani, Armend Sh. (2008)
Annales Mathematicae et Informaticae
Masuda, Tetsu (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Nakazono, Nobutaka (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Horst Alzer, Man Kam Kwong (2022)
Czechoslovak Mathematical Journal
Let where denotes the number of positive divisors of the natural number . We present monotonicity properties of functions defined in terms of . More specifically, we prove that is strictly increasing on , while is strictly decreasing on . These results are then applied to obtain various inequalities, one of which states that the double inequality holds with the best possible constant factors and . Here, denotes Euler’s constant. This refines a result of Salem, who proved the inequalities...
Predrag Rajković, Miomir Stanković, Slađana Marinković (2002)
Matematički Vesnik
Sellami, Mouna, Brahim, Kamel, Bettaibi, Néji (2007)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Mingjin Wang (2010)
Czechoslovak Mathematical Journal
In this paper we give an extension of -Pfaff-Saalschütz formula by means of Andrews-Askey integral. Applications of the extension are also given, which include an extension of -Chu-Vandermonde convolution formula and some other -identities.
Alberto De Sole, Victor G. Kac (2005)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
We study -integral representations of the -gamma and the -beta functions. As an application of these integral representations, we obtain a simple conceptual proof of a family of identities for Jacobi triple product, including Jacobi's identity, and of Ramanujan's formula for the bilateral hypergeometric series.
Lucia Di Vizio, Changgui Zhang (2009)
Annales de l’institut Fourier
This paper is divided in two parts. In the first part we study a convergent -analog of the divergent Euler series, with , and we show how the Borel sum of a generic Gevrey formal solution to a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of a corresponding -difference equation. In the second part, we work under the assumption . In this case, at least four different -Borel sums of a divergent power series solution of an irregular singular...
Krasniqi, Valmir, Shabani, Armend Sh. (2009)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
Brahim, Kamel, Bettaibi, Néji, Sellami, Mouna (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Kim, Taekyun, Adiga, C. (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Ben Hammouda, M.S., Nemri, Akram (2007)
Fractional Calculus and Applied Analysis
Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90In this paper we give the q-analogue of the higher-order Bessel operators studied by I. Dimovski [3],[4], I. Dimovski and V. Kiryakova [5],[6], M. I. Klyuchantsev [17], V. Kiryakova [15], [16], A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [8], and recently by many other authors. Our objective is twofold. First, using the q-Jackson integral and the q-derivative, we aim at establishing some properties of this function with proofs...
Mansour, Toufik, Shabani, Armend Sh. (2009)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Thomas Ernst (2007)
Rendiconti del Seminario Matematico della Università di Padova
Kimio Ueno, Michitomo Nishizawa (1997)
Banach Center Publications
We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product formula) of the Vignéras multiple gamma function by considering the classical limit of the multiple q-gamma function.
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