  P\'{o}lya proved in 1927 that the Riemann hypothesis is equivalent to the
hyperbolicity of all of the Jensen polynomials of degree $d$ and shift $n$ for
the Riemann Xi-function. Recently, Griffin, Ono, Rolen, and Zagier proved that
for each degree $d \geq 1$ all of the Jensen polynomials for the Riemann
Xi-function are hyperbolic except for possibly finitely many $n$. Here we
extend their work by showing the same statement is true for suitable
$L$-functions. This offers evidence for the generalized Riemann hypothesis.
