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BesselJZero

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

BesselJZero[n, k] gives the k-th positive zero of BesselJ[n, x]. Stays symbolic for symbolic arguments.

Examples

No verified examples yet for this function.

Algorithm

besseljzero.c -- BesselJZero[n, k], the k-th positive zero of BesselJ[n, x].

Currently a symbolic placeholder: it stays unevaluated for all arguments so that the Hadamard-product recogniser (Product`BesselZero) can match the canonical infinite product

  Product[1 - x^2/BesselJZero[n,k]^2, {k,1,Inf}] = Gamma[n+1] (2/x)^n BesselJ[n,x].

A future numeric path can evaluate BesselJZero[n, k] for exact numeric n and positive-integer k via McMahon asymptotics + Newton refinement on BesselJ.

Memory contract: takes ownership of res but must not free it; returns NULL (leave unevaluated) or an owned closed form.

Implementation notes

Attributes: Listable, NumericFunction, Protected.

References