Divided-difference equation, inversion, connection, multiplication and linearization formulae of the continuous Hahn and the Meixner-Pollaczek polynomials

作者：Tcheutia D. D.; Sadjang P. Njionou; Koepf W.^*; Foupouagnigni M.

来源：Ramanujan Journal, 2018, 45(1): 33-56.

DOI：10.1007/s11139-016-9870-5

• Meixner-Pollaczek polynomials
• Continuous Hahn polynomials
• Divided-difference equations
• Inversion formula
• Connection formula
• Multiplication formula
• Linearization formula

From the study of various properties of some difference operators, we prove in the first part of this work that the continuous Hahn and the Meixner-Pollaczek polynomials are solutions of a second-order divided-difference equation of hypergeometric- type. Next, using some algorithmic tools, we solve the inversion, connection, multiplication and linearization problems for the continuous Hahn and the Meixner-Pollaczek polynomials.

• 出版日期2018-1