Special Functions (theory and applications)

Daniele Ritelli

  • Date:

    20 DECEMBER 2022
  • Event location: Department of Statistical Science, Alma Mater Studiorum - University of Bologna

  • Type: Cycle 38 - Mandatory Courses

Aims: To instill/promote knowledge, behaviors and skills in the students on special Mathematical functions often found in statistical problems, and improve analytical thinking and conceptualization skills

Learning outcomes: Understand the properties of special functions like Gauss hypergeometric, Legendre functions with their integral representations. Understand the concept of Bessel’s function, Hermite function etc, with its properties like recurrence relations, orthogonal properties, generating functions etc. Understand how special functions are useful in statistical applications.

Final Exam: Individual presentation

Course contents
-Lambert W function
-Eulerian functions: Gamma, Beta, Psi and related functions
-Zeta function
-Bessel functions
-Hypergeometric functions
-Generalized hypergeomtric functions
-Incomplete Eulerian functions
-Multivariate hypergeomteric functions
-Applications to continuos random variables
-Hints to optimization problems