• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.673-693
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• 2005

In this paper, we first find a necessary and sufficient condition for the existence of multiple orthogonal polynomials by the moments of a pair of measures $(d{\mu},\;dv)$ and then give representations for multiple orthogonal polynomials. We also prove four term recurrence relations for multiple orthogonal polynomials of type II and several interesting relations for multiple orthogonal polynomials are given. A generalized recurrence relation for multiple orthogonal polynomials of type I is found and then four term recurrence relations are obtained as a special case.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.299-311
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• 1999

In this paper the single and product moments of order statistics of the doubly truncated Rayleigh distribution are studied. Some recurrence relations of order statistics are derived. Using order statistics, also characterization of the Rayleigh distribution are derived.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.443-462
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• 2014

Using a simple recurrence relation, we give a new method to compute the Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for the Jones polynomials. The method is used to estimate the degree of the Jones polynomials for some families of braids and to obtain general qualitative results.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.851-856
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• 2013

The principal aim of this paper is to investigate a recurrence relation and an integral representation of k-Mittag-Leffler function introduced earlier by Dorrego and Cerutti [2] and several special cases have also been discussed.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.136-145
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• 2024

In this paper we obtained several properties that the characteristic polynomial of the unit-primitive matrix satisfies. In addition, using these properties we have shown that the recurrence relation given as in the formula (1) is true. In fact, Xin and Zhong ([4]) showed it earlier. However, we provide a simpler method here.

• East Asian mathematical journal
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• v.15 no.2
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• pp.191-199
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• 1999

We derive various pure and differential recurrence relations for polynomials of terminating hypergeometric character by making use of Sister Celine's method.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.617-622
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• 2005

In this paper, using Gauss multiplication formula, a recurrence relation for Bernoulli numbers, generalizing Namias' results, is given.

• Journal of Electrochemical Science and Technology
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• v.12 no.2
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• pp.217-224
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• 2021

In this study, Monte Carlo (MC) simulation is conducted with recurrence relation to study the effect of SiO₂ with different particle size and their roles in enhancing the ionic conductivity and lithium transference number of PMMA composite polymer electrolytes (CPEs). The MC simulated ionic conductivity is verified with the measurements from Electrochemical Impedance Spectroscopy (EIS). Then, the lithium transference number of CPEs is calculated using recurrence relation with the MC simulated current density and the reference transference number obtained. Incorporation of micron-size SiO₂ (≤10 ㎛) fillers into the mixture improves the ionic conductivity from 8.60×10^-5 S/cm to 2.35×10^-4 S/cm. The improvement is also observed on the lithium transference number, where it increases from 0.088 to 0.3757. Furthermore, the addition of nano-sized SiO₂ (≤12 nm) fillers further increases the ionic conductivity up towards 3.79×10^-4 S/cm and lithium transference number of 0.4105. The large effective surface area of SiO₂ fillers is responsible for the improvement in ionic conductivity and the transference number in PMMA composite polymer electrolytes.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.99-106
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• 2008

In this paper, we establish some recurrence relations which is satisfied by the quotient moments of the lower record values from the standard generalized extreme value (GEV) distribution.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.1031-1044
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• 2003

In this paper, we establish some recurrence relations of the moments, product moments, percentage points, and modes of order statistics from the transformed exponential distribution.