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

## plane curve in real domain

plot with re2D(x) for 2 curves of real and imag. First graph is real function, second graph is complex function.
1. pow(x,x) function
2. sqrt(x)
3. cbrt(x)
4. Exponential function
5. imag part of Exponential function exp(i*x)
6. Natural logarithm
7. Img part of Circular and Hyperbolic functions in real domain are 0. So only their inverse functions are shown :

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

plot with im2D(x) for 2 curves of real and imag. First graph is real function, second graph is complex function.
1. im2D(x^x)
2. sqrt(i*x)
3. cbrt(i*x)
4. Exponential function exp(i*x)
5. imag part of Exponential function exp(i*x)
6. Natural logarithm log(i*x)
7. real part of Circular and Hyperbolic functions in imag domain are 0. So only their inverse functions are shown :

8. Circular sine
9. Circular cosine
10. Circular tangent
11. Circular cotangent
12. Circular secant
13. Circular cosecant
14. Hyperbolic sine
15. Hyperbolic cosine
16. Hyperbolic tangent
17. Hyperbolic cotangent
18. Hyperbolic secant
19. Hyperbolic cosecant
20. Bessel function of first kind
21. Bessel function of second kind
22. Modified Bessel function of first kind
23. Modified Bessel function of second kind
24. Hankel function of first kind
25. Hankel function of second kind
26. Airy function of first kind
27. Airy function of second kind
28. Elliptic integral of first kind
29. Elliptic integral of second kind
30. Elliptic integral of third kind
31. Jacobi zeta function
32. Jacobi elliptic sine
33. Jacobi elliptic cosine
34. Jacobi delta amplitude
35. Jacobi amplitude
36. Weierstrass elliptic function
37. Gamma function
38. Logarithm of gamma function
39. Riemann zeta function
40. Dirichlet eta function
41. ## 2D surface in complex domain

42. complexplot(z) surface 2D
43. plotcomplex(z) surface 2D
44. WebXR surface 2D

## 3D in complex domain

45. plot complex function with complex3D(i*x) in real and complex domain.

## Complex

1. complex - complex function - complex math
2. complex animate(z) or complex2D(x) for phase animation in complex plane, the independent variable must be z.
3. complex plot(z) for phase and/or modulus in complex plane, the independent variable must be z.
4. plot complex(z) for phase and/or modulus in complex plane, the independent variable must be z.
5. complex2D show re2D(x) and im2D(x) for complex 2 curves of real and imag parts in real and imag domain, 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

## References

1. math handbook content 2 chapter 10 complex function
2. math handbook content 3 chapter 10 complex function
3. math handbook content 4 chapter 10 complex function
4. Complex analysis
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