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On a generalization of close-to-convex functions

Swadesh Kumar Sahoo, Navneet Lal Sharma (2015)

Annales Polonici Mathematici

The paper of M. Ismail et al. [Complex Variables Theory Appl. 14 (1990), 77-84] motivates the study of a generalization of close-to-convex functions by means of a q-analog of the difference operator acting on analytic functions in the unit disk 𝔻 = {z ∈ ℂ:|z| < 1}. We use the term q-close-to-convex functions for the q-analog of close-to-convex functions. We obtain conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate functions in...

On a $q$ -analogue of Sándor's function.

Adiga, C., Kim, T., Somashekara, D.D., Fathima, Syeda Noor (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On a two-variable $p$ -adic $l_{q}$ -function.

Kim, Min-Soo, Kim, Taekyun, Park, D.K., Son, Jin-Woo (2008)

Abstract and Applied Analysis

On another extension of $q$ -Pfaff-Saalschütz formula

Mingjin Wang (2010)

Czechoslovak Mathematical Journal

In this paper we give an extension of $q$ -Pfaff-Saalschütz formula by means of Andrews-Askey integral. Applications of the extension are also given, which include an extension of $q$ -Chu-Vandermonde convolution formula and some other $q$ -identities.

On Bailey pairs and certain q-series related to quadratic and ternary quadratic forms

Alexander E. Patkowski (2011)

Colloquium Mathematicae

We provide a new approach to establishing certain q-series identities that were proved by Andrews, and show how to prove further identities using conjugate Bailey pairs. Some relations between some q-series and ternary quadratic forms are established.

On Heisenberg and local uncertainty principles for the $q$ -Dunkl transform.

Fitouhi, Ahmed, Nouri, Ferjani, Guesmi, Sana (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On interpolation functions of the generalized twisted $(h, q)$ -Euler polynomials.

Park, Kyoung Ho (2009)

Journal of Inequalities and Applications [electronic only]

On multiple interpolation functions of the Nörlund-type $q$ -Euler polynomials.

Açıkgöz, Mehmet, Simsek, Yilmaz (2009)

Abstract and Applied Analysis

On multiple twisted $p$ -adic $q$ -Euler $ζ$ -functions and $l$ -functions.

Kim, Min-Soo, Kim, Taekyun, Son, Jin-Woo (2008)

Abstract and Applied Analysis

On $p$ -adic analogue of $q$ -Bernstein polynomials and related integrals.

Kim, T., Choi, J., Kim, Y.H., Jang, L.C. (2010)

Discrete Dynamics in Nature and Society

On $p, q$ -binomial coefficients.

Corcino, Roberto B. (2008)

Integers

On q-Euler numbers, q-Salié numbers and q-Carlitz numbers

Hao Pan, Zhi-Wei Sun (2006)

Acta Arithmetica

On q-Laplace Transforms of the q-Bessel Functions

Purohit, S., Kalla, S. (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 33D15, 44A10, 44A20The present paper deals with the evaluation of the q-Laplace transforms of a product of basic analogues of the Bessel functions. As applications, several useful special cases have been deduced.

On some Feng Qi type $q$ -integral inequalities.

Brahim, Kamel, Bettaibi, Néji, Sellami, Mouna (2008)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On some inequalities of uncertainty principles type in quantum calculus.

Fitouhi, Ahmed, Bettaibi, Néji, Bettaieb, Rym H., Binous, Wafa (2008)

International Journal of Mathematics and Mathematical Sciences

On Some Partition Functions Related to Some Mock Theta Functions

Alexander E. Patkowski (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We show that some partitions related to two of Ramanujan's mock theta functions are related to indefinite quadratic forms and real quadratic fields. In particular, we examine a third order mock theta function and a fifth order mock theta function.

On the non-quadraticity of values of the q-exponential function and related q-series

Christian Krattenthaler, Igor Rochev, Keijo Väänänen, Wadim Zudilin (2009)

Acta Arithmetica

On the q-exponential of matrix q-Lie algebras

Thomas Ernst (2017)

Special Matrices

In this paper, we define several new concepts in the borderline between linear algebra, Lie groups and q-calculus.We first introduce the ring epimorphism r, the set of all inversions of the basis q, and then the important q-determinant and corresponding q-scalar products from an earlier paper. Then we discuss matrix q-Lie algebras with a modified q-addition, and compute the matrix q-exponential to form the corresponding n × n matrix, a so-called q-Lie group, or manifold, usually with q-determinant...

Orthogonal polynomials and recurrence equations, operator equations and factorization.

Koepf, Wolfram (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Overpartition pairs

Jeremy Lovejoy (2006)

Annales de l’institut Fourier

An overpartition pair is a combinatorial object associated with the $q$ -Gauss identity and the $_{1} ψ_{1}$ summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of recurrences for well-poised basic hypergeometric series and the theory of Bailey chains.

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