The Rayleigh Function

A Property of a Class of Nonlinear Difference Equations

“…Let an = ain(a\b), the Rayleigh function of argument a\b, a odd, b even (see [5]). Then a1=b¡A{a+b) and b "v1 a" = -~T~ 2, akan-k-…”

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“…Properties of <T2n(v) have been discussed in a recent paper by Kishore [2]. We remark that <Tîn{y) is a rational function of v with rational coefficients; the first twelve functions have been computed by Lehmer [3].…”

A Property of the Rayleigh Function

“…Kishore [3] t=l It would be of some interest to know exactly which primes divide the numerator or denominator of atn(v), if v is rational and a^Jy) is reduced to its lowest terms. Restricting ourselves to the prime 2, and using induction on (1.1), we shall find in this paper the exact power of 2 dividing a2niy) when v is a rational number a/b, a odd and b even.…”