Continuous Ackermann function

This is an extension of the Ackermann function to non-integer inputs.

Definition

For non-negative real numbers x and y:

1. x < 1: A(x, y) = x + y + 1
2. x ≥ 1, y < 1: A(x, y) = A(x - 1, y × A(x - 1, 1) - y + 1)
3. x ≥ 1, y ≥ 1: A(x, y) = A(x - 1, A(x, y - 1))

Examples

A(0.5, y) = y + 1.5

A(1.5, y) = 1.5y + 2.5

A(2.5, y) = 9 × 1.5^y - 5

A(e, π) ≈ 42.16412690081622

A(π, e) ≈ 3446961975442.875

A(π, π) (gagpi) ≈ 3446961975442.875