Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 24/Bessel Functions of the First Kind of Order n

Bessel Functions of the First Kind of Order $n$
$24.2$: Series Expansion of Bessel Function of the First Kind

$24.3$: Series Expansion of Bessel Function of the First Kind: Negative Index

$24.4$: Bessel Function of the First Kind of Negative Integer Order

for $n \in \Z_{\ge 0}$.