• Korean Journal of Mathematics
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• v.30 no.1
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• pp.25-42
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• 2022

In this paper, we derive analogues of a couple of classes of infinite series identities with the confluent hypergeometric functions involving Dirichlet characters.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1845-1856
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• 2016

In this paper our aim is to study the classical Bessel-Struve kernel. Monotonicity and log-convexity properties for the Bessel-Struve kernel, and the ratio of the Bessel-Struve kernel and the Kummer confluent hypergeometric function are investigated. Moreover, lower and upper bounds are given for the Bessel-Struve kernel in terms of the exponential function and some $Tur{\acute{a}}n$ type inequalities are deduced.

• Journal of the Korean Statistical Society
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• v.13 no.1
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• pp.42-47
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• 1984

In this paper, the means of the estimators for the coefficient of variation (CV) in an underlying Pareto distribution are expressed in terms of confluent hypergeometric functions. The numericla values of the biases for the CV estimators in the Pareto distribution are also obtained.

• Journal of the Korean Data and Information Science Society
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• v.1
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• pp.67-76
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• 1990

For a two-parameter Pareto distribution, the uniformly minimum variance unbiased estimateors(UMVUE) for the function of the two parameters are expressed in terms of confluent hypergeometric function. The variance of the UMVUE is also expressed in terms of hypergeometric function of several variables. UMVUE's for the ${\gamma}th$ moment about zero and several useful parametric functions, and their variances are obtained as special cases. The estimators of Baxter(1980) and Saksena and Johnson(1984) are special cases of our estimator.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.65-74
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• 2014

The well known quadratic transformation formula due to Gauss: $$(1-x)^{-2a}{_2F_1}\[{{a,b;}\\\hfill{21}{2b;}}\;-\frac{4x}{(1-x)^2}\]={_2F_1}\[{{a,a-b+\frac{1}{2};}\\\hfill{65}{b+\frac{1}{2};}}\;x^2\]$$ plays an important role in the theory of (generalized) hypergeometric series. In 2001, Rathie and Kim have obtained two results closely related to the above quadratic transformation for $_2F_1$. Our main objective of this paper is to deduce some interesting known or new results for the series $_2F_1(x)$ by using the above Gauss's quadratic transformation and its contiguous relations and then apply our results to provide a list of a large number of integrals involving confluent hypergeometric functions, some of which are (presumably) new. The results established here are (potentially) useful in mathematics, physics, statistics, engineering, and so on.

• Bulletin of the Korean Chemical Society
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• v.30 no.2
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• pp.315-318
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• 2009

Some particular bound state energies of an electron, under Coulomb potential field, confined in a two-dimensional circle and a three-dimensional sphere are analytically derived. The derivation shows that the electron cannot be bound in a negative energy state when the circle (or sphere) is smaller than a certain critical size. The critical size dependency on the strength of Coulomb potential and the angular momentum of the electron is also analytically derived. This system mimics quantum dots. Therefore the derivation provides new information on a minimum critical size of quantum dots with hydrogenic impurity.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.25 no.6
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• pp.443-456
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• 1992

For a linear double shelf bottom topography as in the Yellow Sea, the dispersion relation of coastally trapped waves is derived for the general case Including high-frequency and short waves and for the case of low-frequency and long waves. With linear bottom topography, the governing equation is Bessel's equation for the latter case but Hummer's equation for the former case. Hypergeometric Functions, which are the solutions of Hummer's equation, are derived and converted to various special functions for the limiting cases. On a double shelf topography, the divergence effects of horizontal flow are important for the wave dynamics, irrespective of cross-shelf dimensions, while on a single shelf they are usually neglected when the cross-shelf dimension is much smaller than the Rossby deformation radius. The divergence effect allows the existence of Kelvin wave and reduces the phase speeds of continental shelf waves. Finally, the frictionless eigenfunctions are proved to be orthogonal.