1st Edition
I-Function and its Applications
This book presents the essential role of Mathematical Modeling and Computational Methods in representing physical phenomena mathematically, focusing on the significance of the I-function. Serving as a generalized form of special functions, particularly generalised hypergeometric functions, the I-function emerges from solving dual integral equations, prevalent in scenarios like mixed boundary problems in potential theory, energy diffusion, and population dynamics.
• Offers the most recent developments on I-function and their application in mathematical modeling and possible applications to some other research areas
• Expands the area of special functions that have been developed and applied in a variety of fields, such as combinatory, astronomy, applied mathematics, physics, and engineering
• Highlights the importance of fundamental results and techniques based on the theory of complex analysis and emphasize articles devoted to the mathematical aspect and applications
• Shows the importance of fundamental results and techniques derived from the theory of complex analysis, laying the groundwork for further exploration and potential applications of the I-function in solving complex problems
• Discusses dual integral equations solving and its crucial role in various physical phenomena, such as potential theory and population dynamics
Expanding the field of special functions, this book serves as a platform for recent theories and applications, offering students, researchers, and scholars of Mathematics insight into advanced mathematical techniques and their practical implications across various fields.
1.INTRODUCTION 2.TRANSFORMATION OF I-FUNCTION AND H-FUNCTION FOR RATIONAL PARAMETERS 3.CERTAININTEGRALS INVOLVING I-FUNCTION 4. SOME EXPANSION FORMULAS OF I-FUNCTION 5.SINGLE AND DUAL INTEGRAL EQUATIONS INVOLVING I-FUNCTION 6. INTEGRAL EQUATIONS INVOLVING BESSELMAITLAND FUNCTIONS 7. ASSOCIATED GENERATING FUNCTIONS, q AND (p,q)-ANALOGUES OF I-FUNCTION 8. I-FUNCTION APPLICATIONS
Biography
Prof. Vinod Prasad Saxena completed his M.Sc in 1966 with distinction from Jiwaji University Gwalior, Madhya Pradesh. Soon within a span of four years he was awarded Ph.D for his research contribution entitled “Integral Transforms and Their Technical Application’’. At the Post Doctoral level he worked as CSIR senior Research Fellow and Post Doctoral Research Fellow at SATI, Vidisha and M.A. college of Technology Bhopal from May 1969 to July 1971. Besides, Dr. V. P. Saxena was a Visiting Scientist at the University of Cambridge, England. He was also a visiting scientist in 1978 under the British Council UGC (INDIA) Exchange of Young Scientists Programme and worked under Sri James Hill, Professor of LUC Asian University. Besides being a professor, he was Dean, Faculty of Science, Jiwaji University, Gwalior from 1980-1986 and again from 1990-1992. Dr. V. P. Sexena took over as emergency Vice Chancellor, Jiwaji University during August 9, 2000. Dr. V. P. Sexena visited England, China, Singapore, Argentina, Turkey, Cyprus, Germany where he had delivered a series of lectures and presented scores of research papers on Mathematics and Engineering.
Dr. Praveen Agarwal is Vice-Principal and Professor at Anand International College of Engineering, Jaipur, India. He is listed as the World's Top 2% Scientist in 2020, 2021, 2022, and 2023, released by Stanford University. In the 2023 ranking of best scientists worldwide announced by Research.com, he ranked 21st at the India level and 2436th worldwide in Mathematics. He is Editor of Book series Mathematical Modelling & Computational Method for Innovation, Taylor & Francis Group.
Dr. Altaf Ahmad Bhat did his Ph.D. from the School of Mathematics and Allied Sciences, Jiwaji University Gwalior in 2019. He qualified CSIR NET in Mathematics in Dec. 2015. His fields of specialization are Special Functions, Basic Hypergeometric Series, and Fractional Calculus. He has published more than 50 research papers in international repute Journals. He has 8 months of Teaching experience as Teaching Assistant of Mathematics at Department of Mathematics, Islamia College of Science and Commerce – Hawal – Srinagar – Kashmir – India from June 2008 to Jan. 2009 and 5 years of Teaching experience as Assistant Professor of Mathematics at Department of Computer Science and Engineering, Islamic University of Science and Technology – Awantipora – Pulwama – Kashmir – India from March 2011 to Dec. 2015. Presently working as Assistant Professor at the Department of Mathematical Sciences, Islamic University of Science and Technology – Awantipora – Pulwama – Kashmir – India from January 2018 to till date.
