﻿ Complex Functions on plane curve in real domain ﻿﻿﻿ math handbook calculator - Fractional Calculus Computer Algebra System software + + + = ﻿

# Complex Functions

## plane curve in real domain

plot with complex2D(x) for 2 curves of real and imag. First graph is real function, second graph is complex function.
1. pow(x,x) function
2. root(x,x)
3. Exponential function
4. Natural logarithm
5. Img part of Circular and Hyperbolic functions in real domain are 0. So only their inverse functions are shown :

6. Circular sine
7. Circular cosine
8. Circular tangent
9. Circular cotangent
10. Circular secant
11. Circular cosecant
12. Hyperbolic sine
13. Hyperbolic cosine
14. Hyperbolic tangent
15. Hyperbolic cotangent
16. Hyperbolic secant
17. Hyperbolic cosecant
18. Bessel function of first kind
19. Bessel function of second kind
20. Modified Bessel function of first kind
21. Modified Bessel function of second kind
22. Hankel function of first kind
23. Hankel function of second kind
24. Airy function of first kind
25. Airy function of second kind
26. Elliptic integral of first kind
27. Elliptic integral of second kind
28. Elliptic integral of third kind
29. Jacobi zeta function
30. Jacobi elliptic sine
31. Jacobi elliptic cosine
32. Jacobi delta amplitude
33. Jacobi amplitude
34. Weierstrass elliptic function
35. Gamma function
36. Logarithm of gamma function
37. Riemann zeta function
38. Dirichlet eta function
39. ## 2D surface in complex domain

40. complexplot(z) surface 2D
41. WebXR surface 2D

## 3D in complex domain

42. plot complex function with complex3D(x) in real and complex domain.

## References

1. complex - complex function - complex math
2. math handbook chapter 10 complex function
3. complex animate(z) for phase animation, the independent variable must be z.
4. complex plot(z) for phase and/or modulus, the independent variable must be z.
5. complex2D(x) for complex 2 curves of real and imag parts, the independent variable must be x.
6. complex3D(x) for 3 dimensional graph, the independent variable must be x.
7. color WebXR surface of complex function on complex plane
8. Riemann surface - Complex Branches - complex coloring
9. 2D surface - 3D surface
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