In this short note we consider the modified Bessel function of the first kind Iν and we present an alternative derivation of the MacLaurin series expansion of the power Iνr, where r is an arbitrary real (or complex) number. The key tool in our proof is a very old formula of L. Euler deduced in 1748.
- Euler's formula
- Modified Bessel function of the first kind
ASJC Scopus subject areas
- Applied Mathematics