via divided differences

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… ►Let

h(t)={J_{\nu}}^{2}\left(t\right)

and

f(t)=1/(1+t)

. … ►as

y\to\pm\infty

, uniformly for bounded

|x|

; see (5.11.9). … ►Since

\mathscr{M}\mskip-3.0muh_{1}\mskip 3.0mu\left(z\right)

is analytic for

\Re z>-c

by Table 2.5.1, the analytically-continued

\mathscr{M}\mskip-3.0muh_{2}\mskip 3.0mu\left(z\right)

allows us to extend the Mellin transform of

h

via … ►See also Brüning (1984) for a different approach. … ►Put

x=1/\zeta

and break the integration range at

t=1

, as in (2.5.23) and (2.5.24). …