Interlacing of the zeros of contiguous hypergeometric functions

It is well-known that hypergeometric functions satisfy first order difference-differential equations (DDEs) with rational coefficients, relating the first derivative of hypergeometric functions with functions of contiguous parameters (with parameters differing by integer numbers). However, maybe it is not so well known that the continuity of the coefficients of these DDEs implies that the real zeros of such contiguous functions are interlaced. Using this property, we explore interlacing properties of hypergeometric and confluent hypergeometric functions (Bessel functions and Hermite, Laguerre and Jacobi polynomials as particular cases).

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