Confluent Hypergeometric Function - Multiplication Theorem

Multiplication Theorem

The following multiplication theorems hold true:

$\begin{align}U(a,b,z)&= e^{(1-t)z} \sum_{i=0} \frac{(t-1)^i z^i}{i!} U(a,b+i,z t)=\\ &= e^{(1-t)z} t^{b-1} \sum_{i=0} \frac{\left(1-\frac 1 t\right)^i}{i!} U(a-i,b-i,z t).\end{align}$

Read more about this topic: Confluent Hypergeometric Function

Famous quotes containing the word theorem:

“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)