New Addition Formulae Using Hypergeometric Functions Via Gamma Function Representations | Chapter 4 | Mathematics and Computer Science: Research Updates Vol. 6

 

The discovery of a hypergeometric function has provided an intrinsic stimulation in the world of mathematics. It has also motivated the development of several domains such as complex functions, Riemann surfaces, differential equations, difference equations, arithmetic theory and so forth. The global structure of the Gauss hypergeometric function as a complex function, i.e., the properties of its monodromy and the analytic continuation, has been extensively studied by Riemann. His method is based on complex integrals. Moreover, when the parameters are rational numbers, its relation to the period integral of algebraicm curves became clear, and a fascinating problem on the uniformization of a Riemann surface was proposed by Riemann and Schwarz. On the other hand, Kummer has contributed a lot to the research of arithmetic properties of hypergeometric functions. But there, the main object was the Gauss hypergeometric function of one variable. The solution of many problems In this chapter we have developed certain addition formulae using Hypergeometric function in the form of Gamma function. The formulae which are developed here are all new.

 

Author(s) Details

 Salah Uddin
Department of Mathematics, AMET University, Kanathur, Chennai, Tamilnadu, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v6/5678

Probability Laws Derived from the Euler Gamma Function: Understanding through Case Studies | Chapter 1 | Mathematics and Computer Science: Contemporary Developments Vol. 4

Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euleur functions. Application of the functions of Euler contributed to and facilitated the obtaining of important results in statistics and especially in the theories of distribution of sampling. Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. This study aims to understand the Euler Gamma Function and its associated laws of probabilities or probability distributions derived from the function gamma. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euler functions.

 

Author (s) Details

Lansana Toure
Department of Business Administration and LaboMaths, University Julius Nyéréré of Kankan, Kankan, Guinea.

Soumaila Conde
Faculty of Sciences, University Julius Nyéréré of Kankan, Kankan, Guinea.

 

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v4/3688G

The Gamma and Zeta Functions with Infinite Polynomial Products | Chapter 12 | Research and Applications Towards Mathematics and Computer Science Vol. 5

 A numerical hypothesis that was originally put forward in 1859 and is still unsubstantiated as of 2015. The phrase "the Holy Grail of mathematics" has happened used to depict this issue, which is probably the most familiar of all open problems in arithmetic. Although it has connections to different branches of arithmetic, it is often associated with the disposal of prime numbers. The infinite device representation of the gamma function and the zeta function are calm of an exponential and a concerning manipulation of numbers component, and this representation is illustrated by starting with the binomial cooperative and engaging its limitless product form.  It is confirmed, that all these components delineate imaginary ancestries on the critical line, if composed in the form as they are in the functional equating of the zeta function.

Author(s) Details:

Pál Doroszlai,
Fö utca, 8254 Kékkút, Hungary.

Horacio Keller,
Swiss Federal Institute of Technology, Switzerland.

Please see the link here: https://stm.bookpi.org/RATMCS-V5/article/view/12322