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- (2+ 1) dimensional variable coefficient KdV equation (1)
- Anti-mathematics (1)
- Diophantine equations (1)
- Generalized Laguerre matrix method (1)
- Generating function (1)
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- H-function (1)
- Hirota’s bilinear form (1)
- I-function (1)
- Laguerre polynomials (1)
- Laguerre-Gould Hopper polynomials (1)
- Lauricella function (1)
- Linear differential-difference equations with variable coefficients (1)
- Mathematics (1)
- Mellin-Barnes Contour integral (1)
- Number Theory (1)
- Operational matrices (1)
- Painlevé property (1)
- Paradoxism (1)
- Soliton solution (1)
- Summation formulae (1)
- Summation theorems (1)
- Symbolic computation (1)
- Unsolved problems (1)
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Articles 1 - 6 of 6
Full-Text Articles in Special Functions
Certain Results For The Laguerre-Gould Hopper Polynomials, Subuhi Khan, Ahmed A. Al-Gonah
Certain Results For The Laguerre-Gould Hopper Polynomials, Subuhi Khan, Ahmed A. Al-Gonah
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we derive generating functions for the Laguerre-Gould Hopper polynomials in terms of the generalized Lauricella function by using series rearrangement techniques. Further, we derive the summation formulae for that polynomials by using different analytical means on its generating function or by using certain operational techniques. Also, generating functions and summation formulae for the polynomials related to Laguerre-Gould Hopper polynomials are obtained as applications of main results.
Integrability And Exact Solutions For A (2+1)-Dimensional Variable-Coefficient Kdv Equation, Zhang Yu, Xu Gui-Qiong
Integrability And Exact Solutions For A (2+1)-Dimensional Variable-Coefficient Kdv Equation, Zhang Yu, Xu Gui-Qiong
Applications and Applied Mathematics: An International Journal (AAM)
By using the WTC method and symbolic computation, we apply the Painlevé test for a (2+1)-dimensional variable-coefficient Kortweg-de Vries (KdV) equation, and the considered equation is found to possess the Painlevé property without any parametric constraints. The auto-Bǎcklund transformation and several types of exact solutions are obtained by using the Painlevé truncated expansion method. Finally, the Hirota’s bilinear form is presented and multi-soliton solutions are also constructed.
The Generalized Laguerre Matrix Method Or Solving Linear Differential-Difference Equations With Variable Coefficients, Z. K. Bojdi, S. Ahmadi-Asl, A. Aminataei
The Generalized Laguerre Matrix Method Or Solving Linear Differential-Difference Equations With Variable Coefficients, Z. K. Bojdi, S. Ahmadi-Asl, A. Aminataei
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a new and efficient approach based on the generalized Laguerre matrix method for numerical approximation of the linear differential-difference equations (DDEs) with variable coefficients is introduced. Explicit formulae which express the generalized Laguerre expansion coefficients for the moments of the derivatives of any differentiable function in terms of the original expansion coefficients of the function itself are given in the matrix form. In the scheme, by using this approach we reduce solving the linear differential equations to solving a system of linear algebraic equations, thus greatly simplify the problem. In addition, several numerical experiments are given to …
On Some Summation Formulae For The I-Function Of Two Variables, Shantha K. Kumari, Vasudevan T. M. Nambisan
On Some Summation Formulae For The I-Function Of Two Variables, Shantha K. Kumari, Vasudevan T. M. Nambisan
Applications and Applied Mathematics: An International Journal (AAM)
In this research paper, we aim to establish three interesting summation formulae for the I-function of two variables recently introduced in the literature. The results are derived with the help of classical summation theorems due to Watson, Dixon and Whipple. A few known results are also obtained as special cases of our main findings. Since the I-function of two variables is the most generalized function of two variables and it includes as special cases many of the known functions appearing in the literature, the results derived in this paper will therefore serve as the key formulas from which a large …
Collected Papers, Vol. V, Florentin Smarandache
Collected Papers, Vol. V, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Solving Diophantine Equations, Florentin Smarandache, Octavian Cira
Solving Diophantine Equations, Florentin Smarandache, Octavian Cira
Branch Mathematics and Statistics Faculty and Staff Publications
In recent times, we witnessed an explosion of Number Theory problems that are solved using mathematical software and powerful computers. The observation that the number of transistors packed on integrated circuits doubles every two years made by Gordon E. Moore in 1965 is still accurate to this day. With ever increasing computing power more and more mathematical problems can be tacked using brute force. At the same time the advances in mathematical software made tools like Maple, Mathematica, Matlab or Mathcad widely available and easy to use for the vast majority of the mathematical research community. This tools don’t only …