Some Unified and Generalized Kummer's Second Summation Theorems with Applications in Laplace Transform Technique


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Authors

  • M. I. Qureshi Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi, India
  • M. S. Baboo School of Basic Sciences and Research, Sharda University, Greater Noida, Uttar Pradesh, India

Keywords:

Gauss and Kummer hypergeometric functions, Legendre duplication formula, Pfaff-Kummer's linear hypergeometric transformation, Principle of analytic continuation, Laplace transforms

Abstract

Some significant hypergeometric summation theorems with suitable convergence conditions, are obtained in the present study; analogous to summation theorems for Gauss function ${_2F_1(\frac{1}{2})}$ presented by Brychkov, Prudnikov  et~al. and derived by Fox, Rakha-Rathie. By means of these summation theorems we also find the Laplace transforms of Kummer's confluent hypergeometric function $_1F_1$ in closed form.

 

 

Author Biographies

M. I. Qureshi, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi, India

 

 

M. S. Baboo, School of Basic Sciences and Research, Sharda University, Greater Noida, Uttar Pradesh, India

 

 

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Published

29-02-2016

How to Cite

M. I. Qureshi, & M. S. Baboo. (2016). Some Unified and Generalized Kummer’s Second Summation Theorems with Applications in Laplace Transform Technique. International Journal of Mathematics And Its Applications, 4(1 - C), 45–52. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/593

Issue

Vol. 4 No. 1 - C (2016)

Section

Research Article

License

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