13 Confluent Hypergeometric FunctionsKummer Functions13.11 Series13.13 Addition and Multiplication Theorems

13.12.1 | $$M(a,b,z)M(-a,-b,-z)+\frac{a(a-b){z}^{2}}{{b}^{2}(1-{b}^{2})}M(1+a,2+b,z)M(1-a,2-b,-z)=1.$$ | ||

For generalizations of this quadratic relation see Majima et al. (2000).

For integral representations, integrals, and series containing products of $M(a,b,z)$ and $U(a,b,z)$ see Erdélyi et al. (1953a, §6.15.3).