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Analytical Approach to Extended Beta and Hypergeometric Functions and Their Applications | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 شهریور 1405 اصل مقاله (1.35 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.71121.3576 | ||
| نویسندگان | ||
| Syed Ali Haider Shah1؛ Mujahid Hussain Shah1؛ Shahid Mubeen2؛ Imran Siddique* 3؛ Barno Abduvalieva4 | ||
| 1Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan. | ||
| 2Department of Mathematics, Baba Guru Nanak University, Pakistan. | ||
| 31. Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan. 2. Research Center of Applied Mathematics, Khazar University, Baku, AZ 1096, Azerbaijan. 3. Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen Iraqi University, Nasiriyah, Thi-Qar, 64001, Iraq. | ||
| 4Department of Mathematics, National Pedagogical University of Uzbekistan named after Nizami, Tashkent, Uzbekistan. | ||
| چکیده | ||
| In this paper, we introduce a new generalization of beta and Gauss hypergeometric functions in terms of k > 0 parameter, also investigate numerical and graphical representations for dierent values of k-parameter. For numerical veri cation of the analytical results, we implemented a 20-point Gauss-Legendre quadrature scheme in Python. Particularly, the k-parameter has a suppressive eect due to its role in scaling the exponent and argument of the hypergeometric function. This makes the function highly tunable, which is important in applications requiring shape control and heavy-tailed behavior modeling. The plots illustrate these relationships vividly, supporting the mathematical formulation through visual interpretation. In this work, we examine several fundamental properties of the newly introduced generalized extended beta k-function, including its integral representations, Mellin transforms, inverse Mellin transforms, and associated summation formulas. Furthermore, we establish Laplace transforms, the RiemannLiouville fractional integral, and a variety of integrals involving the Gauss hypergeometric k-function, along with results concerning the derivatives of the generalized extended Gauss hypergeometric k-function. | ||
| کلیدواژهها | ||
| Hypergeometric k-functions؛ Extended gamma k-function؛ Extended beta k-function؛ Mellin transform؛ Laplace transform | ||
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آمار تعداد مشاهده مقاله: 3 تعداد دریافت فایل اصل مقاله: 6 |
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