# Three-term recurrence for Bateman F

From specialfunctionswiki

## Theorem

The following formula holds: $$n^2 F_n(z) = -(2n-1)z F_{n-1}(z)+(n-1)^2 F_{n-2}(z),$$ where $F_n$ denotes the Bateman F.

## Proof

## References

- 1960: Earl David Rainville:
*Special Functions*... (previous) ... (next): $148. (3)$