The expansions (14.13.1) and (14.13.2) are derived in §3.5 of
Erdélyi et al. (1953a), but without any statement of conditions on and . To
obtain these conditions we see that by combination of (14.13.1) and (14.13.2),
We then apply the results given in the last paragraph of §15.2(i), and subsequently
take real and imaginary parts in the case of conditional convergence.
The conditions for convergence of the Fourier expansions (14.13.1), (14.13.2)
have been corrected. Originally it was stated that they converge
“…conditionally when is real and .” It has been corrected
to read “If then they converge, but, if
, they do not converge absolutely.”
Suggested 2021-09-08 by Hans Volkmer
Clarification (effective with 1.0.1):
The conditions for convergence of the expansions in this subsection were clarified.