Connection Formulas on Kummer’s Solutions and their Extension on Hypergeometric Function

Authors

  • Madhav Prasad Poudel School of Engineering, Pokhara University, Pokhara-30, Kaski, Nepal
  • Narayan Prasad Pahari Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu, Nepal
  • Ganesh Basnet Department of Mathematics, Tribhuvan University, Tri-Chandra Campus, Kathmandu, Nepal
  • Resham Poudel Department of Mathematics, Tribhuvan University, Tri-Chandra Campus, Kathmandu, Nepal

DOI:

https://doi.org/10.3126/njmathsci.v4i2.60177

Keywords:

Hypergeometric function, Kummer's formula, Connection formula

Abstract

Hypergeometric functions are transcendental functions that are applicable in various branches of mathematics, physics, and engineering. They are solutions to a class of differential equations called hypergeometric differential equations. Kummer obtained six solutions for the hypergeometric differential equation and twenty connection formulae. This research work has extended those connection formulas to other six solutions   y1(x), y2(x), y3(x), y4(x), y5(x) and y6(x) show that each solution can be expressed in terms of linear relationship among three of the other solutions. 

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Published

2023-12-08

How to Cite

Poudel, M. P., Pahari, N. P., Basnet, G., & Poudel, R. (2023). Connection Formulas on Kummer’s Solutions and their Extension on Hypergeometric Function. Nepal Journal of Mathematical Sciences, 4(2), 83–88. https://doi.org/10.3126/njmathsci.v4i2.60177

Issue

Vol. 4 No. 2 (2023)

Section

Articles

License

© School of Mathematical Sciences, Tribhuvan University