Probability and special functions of mathematical physics

Zaliapin V.I.

454080, Chelyabinsk, 76 Lenin av., SUSU, Institute of Natural Sciences and Mathematics

The report proposes a method for studying special functions of mathematical physics based on their probabilistic interpretation. The constructed class of functions (the so-called Poisson walk functions) includes classical special functions and generalizes their properties. Using well-studied stochastic constructions of randomized random walk, it is possible to take a fresh look at complex relations and formulas of the theory of special functions, decipher known relations and asymptotics, study their properties.


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