The main objective of the training workshop is to provide a comprehensive overview of special functions and their applications in other branches of Science with an emphasis on computing special functions with MATLAB. The workshop will provide an excellent opportunity for participants to meet and exchange ideas of common interests and to discuss new challenges faced by our academic community working in this area from different institutions and universities around the world. The training will motivate and educate the participants to undertake research in this field. The expected outcome from this event is for the participants to be able to confidently carry out research in this field and also apply it to real-world problems. The procedure we intend to use in achieving this is by having resource persons who are knowledgeable in this field to deliver their talk and guide the participants on how to apply the special functions to real-life problems. Our desire is to leave an impact on the students and researchers to help them with research in the field of computing special functions and their applications.  

Special Functions

Special functions arise in many problems of pure and applied mathematics, mathematical statistics, physics, and engineering. Beyond the well-known elementary functions, special functions gather a great variety of mathematical functions of great importance due to their applications in the fields of physics, mathematics and engineering, and their notation has been consolidated over time. The recent developments in the field of special functions, including classical special functions (gamma, beta, polygamma; higher logarithms; error or incomplete gamma and beta functions; and q-gamma and q-beta functions) or other typical special functions (elliptic integrals; cylinder, hypergeometric and generalized hypergeometric functions; and basic hypergeometric functions) are widely used in Physical Sciences and Engineering. In addition, introducing new parameters such as Mittag–Leffler function; Riemann and Hurwitz zeta functions; and Apell, Horn, and Lauricella functions can be introduced and in their applications in the form of solutions of FDE, PDE and ODE may lead to generalized new and extended the results. The workshop will focus on theoretical and computational aspects of special functions & their applications and use in various areas of mathematics.

About the workshop

The training workshop will be held through our own platform MathTechEdu in virtual mode. Participants will log in to their accounts to attend the sessions. All the content presented in the training workshop will be shared with all the registered participants. Recording of each session will be available in the participant's account. Attendance of each participant during the session is mandatory. The e-certificate of participation will be awarded after attending the training/ workshop successfully. Participants will get everything in their accounts.

Contents

Gamma Functions: Gamma function, incomplete gamma function, Inverse incomplete gamma function, Logarithm of gamma function, Digamma and polygamma functions

Beta Functions: Beta function, incomplete beta function, Beta inverse cumulative distribution function, Logarithm of beta function

Bessel Functions: Airy Functions, Bessel function of third kind (Hankel function), Modified Bessel function of the first kind, Modified Bessel function of the second kind, Bessel function of the second kind

Error Functions: Error function, Complementary error function, Inverse complementary error function, Scaled complementary error function, Inverse error function

Other Special Functions: Jacobi elliptic functions, Complete elliptic integrals of first and second kind, Exponential integral function, Associated Legendre functions

Extended and Generalized Special Function: Mittag-Leffler Functions, Wright Function, etc and their applications