This work studies the local theory for certain Rankin-Selberg convolutions for the standard $L$-function of degree $21n$ of generic representations of $\textnormal{SO}_{2\ell +1}(F)\times \textnormal{GL}_n(F)$ over a local field $F$. The local integrals converge in a half-plane and continue meromorphically to the whole plane. One main result is the existence of local gamma and $L$-factors. The gamma factor is obtained as a proportionality factor of a functional equation satisfied by the local integrals. In addition, Soudry establishes the multiplicativity of the gamma factor ($1
Introduction and preliminaries The integrals to be studied Estimates for
Whittaker functions on $G_\ell$ (nonarchimedean case) Estimates for Whittaker
functions on $G_\ell$ (archimedean case) Convergence of the integrals
(nonarchimedean case) Convergence of the integrals (archimedean case)
$A(W,\xi_{\tau,s})$ can be made constant (nonarchimedean case) An analog in
the archimedean case Uniqueness theorems Application of the intertwining
operator Definition of local factors Multiplicativity of the $\gamma$-factor
(case $\ell < n$, first variable) The unramified computation.
