• 한국측량학회지
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• 제25권1호
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• pp.63-68
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• 2007

The computations of an ultra-high degree associated Legendre functions and its first derivative up to degree and order of 10800 are reported. Not only the magnitude of orders for the ultra-high degree calculation is presented but the numerical stability and accuracy of the computed values are described in detail. The accuracy on the order of $10^{-25}\;and\;10^{-15}$ was obtained for the values of Legendre function and the first derivatives of Legendre functions, respectively. The computable highest degree and order of Legendre function in terms of latitudes and the linear relationship between the magnitude of the function with respect to degrees and orders is found. It is expected that the computed Legendre functions contribute in many geodetic and geophysical applications for simulations as well as theoretical verifications.

• 대한수학회논문집
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• 제22권2호
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• pp.219-225
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• 2007

Since the time of Euler, the dilogarithm and polylogarithm functions have been studied by many mathematicians who used various notations for the dilogarithm function $Li_2(z)$. These functions are related to many other mathematical functions and have a variety of application. The main objective of this paper is to present corrected versions of two equivalent factorization formulas involving the Legendre's Chi-function $\chi_2$ and an evaluation of a class of integrals which is useful to evaluate some integrals associated with the dilogarithm function.

• Kyungpook Mathematical Journal
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• 제10권1호
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• pp.53-57
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• 1970

• Kyungpook Mathematical Journal
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• 제10권2호
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• pp.107-113
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• 1970

• 전산구조공학
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• 제10권1호
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• pp.159-171
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• 1997

본 연구에서는 구형 공동을 가진 횡 방향 등방성 매체(transversely isotropic medium)에 한 방향의 인장과 평면 전단력을 각각 가한 후의 응력 분포를 고찰하였다. 이 연구에서 사용된 접근방법은 이론적 해석과 수치해석적 고찰을 병행하였다. 이론적 해석방법은 1종, 2종 Legendre함수를 이용한 potential function에 기초하였고, 수치해석적 방법은 유한차분법을 이용하였다. 다섯가지 이방성 재료에 대하여 두가지 하중 조건에 의한 수치해석 결과가 제시되었다.

• 대한수학회논문집
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• 제34권1호
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• pp.169-183
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• 2019

The main aim of this paper is to establish a new class of integrals involving the generalized Galu$Galu{\grave{e}}$-type Struve function with the different type of polynomials such as Jacobi, Legendre, and Hermite. Also, we derive the integral formula involving Legendre, Wright generalized Bessel and generalized Hypergeometric functions. The results obtained here are general in nature and can deduce many known and new integral formulas involving the various type of polynomials.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.207-218
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• 2014

The principal object of this paper is to study a class of matrix polynomials associated with Humbert polynomials. These polynomials generalize the well known class of Gegenbauer, Legendre, Pincherl, Horadam, Horadam-Pethe and Kinney polynomials. We shall give some basic relations involving the Humbert matrix polynomials and then take up several generating functions, hypergeometric representations and expansions in series of matrix polynomials.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권2호
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• pp.127-135
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• 2001

The main object of this paper is to present a transformation formula for a finite series involving $_3F_2$ and some identities associated with the binomial coefficients by making use of the theory of Legendre polynomials $P_{n}$(x) and some summation theorems for hypergeometric functions $_pF_q$. Some integral formulas are also considered.

• Journal of Astronomy and Space Sciences
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• 제32권3호
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• pp.247-256
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• 2015

In this work, an efficient method with which to evaluate the high-degree-and-order gravitational harmonics of the non-sphericity of a central body is described and applied to state predictions of a lunar orbiter. Unlike the work of Song et al. (2010), which used a conventional computation method to process gravitational harmonic coefficients, the current work adapted a well-known recursion formula that directly uses fully normalized associated Legendre functions to compute the acceleration due to the non-sphericity of the moon. With the formulated algorithms, the states of a lunar orbiting satellite are predicted and its performance is validated in comparisons with solutions obtained from STK/Astrogator. The predicted differences in the orbital states between STK/Astrogator and the current work all remain at a position of less than 1 m with velocity accuracy levels of less than 1 mm/s, even with different orbital inclinations. The effectiveness of the current algorithm, in terms of both the computation time and the degree of accuracy degradation, is also shown in comparisons with results obtained from earlier work. It is expected that the proposed algorithm can be used as a foundation for the development of an operational flight dynamics subsystem for future lunar exploration missions by Korea. It can also be used to analyze missions which require very close operations to the moon.

• 대한수학회논문집
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• 제32권2호
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• pp.305-319
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• 2017

Recently many authors have investigated so-called Aleph (${\aleph}$)-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph (${\aleph}$)-function. Precisely, integrals with product of Aleph (${\aleph}$)-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.