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Let JQ, be the Bessel function of the first kind of order a > —1. Then Goi(z) := z~Ja(z) is an entire function whose zeros are all real. We note that under appropriate conditions, the Lagrange interpolant of / : R —*• C in the zeros of Ga(Tz) where r > 0 is an entire function of exponential type r. We denote it by LT,a(/;2) and study the mean convergence of LTja(f'r) to / as r —> oo. We obtain a theorem which is analogous to two well-known results, one due to J. Marcinkiewicz and another due to R. Askey. Some of the lemmas which we need for our proof of the theorem are results of independent interest; for example, Lemma 13 is an extension of the Whittaker-Shannon sampling theorem.

Lagrange interpolation in the zeros of Bessel functions by entire functions of exponential type and mean convergence