• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.345-354
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• 2020

In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of ₂𝜓₂ series $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a,c;q)_n}{(b,d;q)_n}}z^n$$ and Ramanujan's sum $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a;q)_n}{(b;q)_n}}z^n$$.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.87-97
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• 2017

In [9], we computed shadows of the second order mock theta functions and showed that they are essentially same with the shadow of a mock theta function related to the Mathieu moonshine phenomenon. In this paper, we further survey the second order mock theta functions on their quantum modularity and their behavior in the lower half plane.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.173-184
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• 2016

Mock theta functions are the most interesting topic mentioned in Ramanujan's Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the present research articles we have made an attempt to develop continued fractions representation of all the existing Mock theta functions.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.249-262
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• 2014

In this paper, we have developed a non-homogeneous q-difference equation of first order for the generalized Mock theta function of order eight and besides these established limiting case of Mock theta functions of order eight. We have also established identities for Partial Mock theta function and Mock theta function of order eight and provided a number of cases of the identities.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.349-361
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• 2017

By means of the Oberhettinger integral, certain generalized integral formulae involving product of generalized k-Bessel function $w^{{\gamma},{\alpha}}_{k,v,b,c}(z)$ and general class of polynomials $S^m_n[x]$ are derived, the results of which are expressed in terms of the generalized Wright hypergeometric functions. Several new results are also obtained from the integrals presented in this paper.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.323-329
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• 2021

The main object of the present paper is to investigate some radius results of the functions f(z) = z + Σ^∞_n=2 a_nzⁿ(|z| < 1) with |a_n| ≤ n for all n ∈ ℕ. Some applications for certain operator defined through convolution are also considered.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.167-181
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• 2021

In this paper, the Saigo's k-fractional integral and derivative operators involving k-hypergeometric function in the kernel are applied to the generalized k-Bessel function; results are expressed in term of k-Wright function, which are used to present image formulas of integral transforms including beta transform. Also special cases related to fractional calculus operators and Bessel functions are considered.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.65-94
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• 2016

In 1812, Gauss obtained fifteen contiguous functions relations. Later on, 1847, Henie gave their q-analogue. Recently, good progress has been done in finding more contiguous functions relations by employing results due to Gauss. In 1999, Cho et al. have obtained 24 new and interesting contiguous functions relations with the help of Gauss's 15 contiguous relations. In fact, such type of 72 relations exists and therefore the rest 48 contiguous functions relations have very recently been obtained by Rakha et al.. Thus, the paper is in continuation of the paper [16] published in Computer & Mathematics with Applications 61 (2011), 620.629. In this paper, first we obtained 15 q-contiguous functions relations due to Henie by following a different method and then with the help of these 15 q-contiguous functions relations, we obtain 72 new and interesting q-contiguous functions relations. These q-contiguous functions relations have wide applications.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2155-2163
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• 2017

Zwegers showed that a mock theta function can be completed to form essentially a real analytic modular form of weight 1/2 by adding a period integral of a certain weight 3/2 unary theta series. This theta series is related to the holomorphic modular form called the shadow of the mock theta function. In this paper, we discuss the computation of shadows of the second order mock theta functions and show that they share the same shadow with a mock theta function which appears in the Mathieu moonshine phenomenon.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.515-528
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• 2006

This article presents a unified analytical solution for the analysis of thermal deformations and stresses in elastic annular disks with arbitrary cross-sections of continuously variable thickness. The annular disk is assumed to be under steady heat flow conditions, in which the inner surface of the annular disk is at an initial temperature and the outer surface at zero temperature. The governing second-order differential equation is derived from the basic equations of the thermal annular disks and solved with the aid of some hypergeometric functions. Numerical results for thermal stresses and displacement are given for various annular disks. These disks include annular disks of thickness profiles in the form of general parabolic and exponential functions. Additional annular disks with nonlinearly variable thickness and uniform thickness are also included.