Unlock advanced wave equation solutions with our Spherical Hankel Function Calculator. Easily compute ^{(1)}(z)$ and ^{(2)}(z)$ for complex numbers and integer orders, vital for fields like acoustics, electromagnetism, and quantum mechanics. Get precise results for both first and second kinds instantly!
Formula:
The Spherical Hankel Functions are solutions to the spherical Bessel differential equation. They are defined in terms of spherical Bessel functions of the first kind ((z)$) and second kind ((z)$) as follows:
- First Kind: ^{(1)}(z) = j_n(z) + i y_n(z)$
- Second Kind: ^{(2)}(z) = j_n(z) - i y_n(z)$
Where:
- $ is the order (a non-negative integer).
- $ is the complex argument ( = x + iy$).
- $ is the imaginary unit (^2 = -1$).
This calculator specifically implements the exact formulas for order n=0.