Digital Library of Mathematical Functions
About the Project
NIST
10 Bessel FunctionsModified Bessel Functions

§10.36 Other Differential Equations

The quantity λ2 in (10.13.1)–(10.13.6) and (10.13.8) can be replaced by -λ2 if at the same time the symbol 𝒞 in the given solutions is replaced by 𝒵. Also,

10.36.1 z2(z2+ν2)w′′+z(z2+3ν2)w-((z2+ν2)2+z2-ν2)w=0,
w=𝒵ν(z),
10.36.2 z2w′′+z(1±2z)w+(±z-ν2)w=0,
w=z𝒵ν(z).

Differential equations for products can be obtained from (10.13.9)–(10.13.11) by replacing z by z.