ISSN 2394-5125
 

Research Article 


HYPERGEOMETRIC FUNCTION AND ITS APPLICATIONS

Dr. Pooja Singh.

Abstract
In this paper, we define an extended Pochhammer symbol by using a known extension of the gamma function involving the modified Bessel function. We apply extended Pochhammer symbol, to explore the resultant extension of the generalized hypergeometric function and its various special cases. By using this, we get different types of relations, formulas and theorems, as: summation, transformation, expansion theorems, integrals involving and representing special functions and/or hypergeometric functions etc.; for various types of extensions of hypergeometric functions, with emphasis on their Applications.
We investigate integral representations of Appell Functions F1, F2 and F3 which is positive definite matrices and real symmetric. The results deal with real valued scalar functions of matrix argument in real case with matrices order unity. The objective of this paper is to determine special integral representations of Appell functions F1, F2 and F3 of two matrix arguments.

Key words: Gamma function and its extension, Generalized hypergeometric functions, Confluent Hypergeometric function, Special Functions.


 
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Pubmed Style

Dr. Pooja Singh. HYPERGEOMETRIC FUNCTION AND ITS APPLICATIONS. JCR. 2020; 7(19): 3130-3137. doi:10.31838/jcr.07.19.375


Web Style

Dr. Pooja Singh. HYPERGEOMETRIC FUNCTION AND ITS APPLICATIONS. http://www.jcreview.com/?mno=122809 [Access: September 15, 2020]. doi:10.31838/jcr.07.19.375


AMA (American Medical Association) Style

Dr. Pooja Singh. HYPERGEOMETRIC FUNCTION AND ITS APPLICATIONS. JCR. 2020; 7(19): 3130-3137. doi:10.31838/jcr.07.19.375



Vancouver/ICMJE Style

Dr. Pooja Singh. HYPERGEOMETRIC FUNCTION AND ITS APPLICATIONS. JCR. (2020), [cited September 15, 2020]; 7(19): 3130-3137. doi:10.31838/jcr.07.19.375



Harvard Style

Dr. Pooja Singh (2020) HYPERGEOMETRIC FUNCTION AND ITS APPLICATIONS. JCR, 7 (19), 3130-3137. doi:10.31838/jcr.07.19.375



Turabian Style

Dr. Pooja Singh. 2020. HYPERGEOMETRIC FUNCTION AND ITS APPLICATIONS. Journal of Critical Reviews, 7 (19), 3130-3137. doi:10.31838/jcr.07.19.375



Chicago Style

Dr. Pooja Singh. "HYPERGEOMETRIC FUNCTION AND ITS APPLICATIONS." Journal of Critical Reviews 7 (2020), 3130-3137. doi:10.31838/jcr.07.19.375



MLA (The Modern Language Association) Style

Dr. Pooja Singh. "HYPERGEOMETRIC FUNCTION AND ITS APPLICATIONS." Journal of Critical Reviews 7.19 (2020), 3130-3137. Print. doi:10.31838/jcr.07.19.375



APA (American Psychological Association) Style

Dr. Pooja Singh (2020) HYPERGEOMETRIC FUNCTION AND ITS APPLICATIONS. Journal of Critical Reviews, 7 (19), 3130-3137. doi:10.31838/jcr.07.19.375