On the wave-equation applications in "Extended Riemann Bessel functions"

Independent technical comment on M. T. Boudjelkha, Extended Riemann Bessel functions, Discrete and Continuous Dynamical Systems, Supplement 2005, 121–130 (DOI: 10.3934/proc.2005.2005.121). Exact counterexamples at b=1 and nu=4 show that representations (40) and (46) fail the wave equation; (46) also violates its homogeneous Neumann boundary condition, and (40) fails the zero initial displacement. Locally finite sums of delayed Bessel boundary data provide corrected classical solutions for nu>2, with proofs of the equation, initial and boundary conditions, uniqueness, and agreement with the Laplace transforms. A missing m=0 summand in (16) and a missing argument factor in (38) are recorded separately. The scope is limited to these formulas and does not invalidate the entire special-function framework. Includes the revised five-page PDF and LaTeX source ZIP with an exact-rational verification script and recorded numerical output. Version 1.0. This independent preprint has not been peer reviewed and is not a publisher-issued corrigendum. The note discloses AI assistance in mathematical analysis, development and checking of the arguments, numerical verification, drafting and English improvement, with author responsibility for the mathematical statements, proofs and final content.