Probabilistic proof of a Hankel transform of Laguerre polynomials

✍ Scribed by S.H. Ong

• Book ID: 104135300
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 74 KB
• Volume: 336
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(99)00020-4

✦ Synopsis

This paper shows that the Hankel transform of order may be interpreted as a mixture formulation of a function with the non-central gamma as mixing distribution. This result is applied to give a probabilistic derivation of the Hankel transform of order of generalized Laguerre polynomials. The application of this result to numerically evaluate the Hankel transform or a Hankel-type integral by the Monte Carlo method is also brie#y examined.