Dharma P Gupta and Martin E Muldoon 2000 J. Phys. A: Math. Gen. 33 1363 doi:10.1088/0305-4470/33/7/306
Riccati equations and convolution formulae for functions of Rayleigh type
Dharma P Gupta and Martin E Muldoon
Show affiliationsKishore (1963 Proc. Am. Math. Soc. 14 527) considered the Rayleigh functions 
n (
) = 
k = 1 
j k -2n ,n = 1,2, ... , where ±j k are the (non-zero) zeros of the Bessel function J (z ) and provided a convolution-type sum formula for finding n in terms of 1 , ... , n -1 . His main tool was the recurrence relation for Bessel functions. Here we extend this result to a larger class of functions by using Riccati differential equations. We get new results for the zeros of certain combinations of Bessel functions and their first and second derivatives as well as recovering some results of Buchholz for zeros of confluent hypergeometric functions.
- PACS
- MSC
-
33C15 Confluent hypergeometric functions, Whittaker functions, 1F1
- Subjects
- Dates
-
Issue 7 (25 February 2000)
Received 12 October 1999
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Riccati equations and convolution formulae for functions of Rayleigh type
Dharma P Gupta and Martin E Muldoon 2000 J. Phys. A: Math. Gen. 33 1363
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