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Complex Functions

Content

on plane curve 2D in real domain

in WebXR Surface 2D

1. Exponential function
2. Natural logarithm
3. Circular sine
4. Circular cosine
5. Circular tangent
6. Circular cotangent
7. Circular secant
8. Circular cosecant
9. Hyperbolic sine
10. Hyperbolic cosine
11. Hyperbolic tangent
12. Hyperbolic cotangent
13. Hyperbolic secant
14. Hyperbolic cosecant
15. Bessel function of first kind
16. Bessel function of second kind
17. Modified Bessel function of first kind
18. Modified Bessel function of second kind
19. Hankel function of first kind
20. Hankel function of second kind
21. Airy function of first kind
22. Airy function of second kind
23. Elliptic integral of first kind
24. Elliptic integral of second kind
25. Elliptic integral of third kind
26. Jacobi zeta function
27. Jacobi elliptic sine
28. Jacobi elliptic cosine
29. Jacobi delta amplitude
30. Jacobi amplitude
31. Weierstrass elliptic function
32. Gamma function
33. Logarithm of gamma function
34. Riemann zeta function
35. Dirichlet eta function

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Complex

1. complex2D
   1. re2D(log(x)) show 2 curves of real and imag values in real domain.
   2. im2D(log(x)) show 2 curves of real and imag values in imag domain.
   3. for complex 2 curves of real and imag values in real and imag domain.
   4. complex coloring
   5. color WebXR surface of complex function on complex plane
   6. complex animate(z) or complex2D(z) for phase animation in complex plane, the independent variable must be z.
   7. complex plot(z) for phase and/or modulus in complex plane, the independent variable must be z.
   8. plot complex(z) for phase and/or modulus in complex plane, the independent variable must be z.
2. complex3D
   1. complex function
   2. Complex Branches
   3. Riemann surface
   4. complex3D(x) for 3 dimensional graph in real, imag and complex domain, where the independent variable must be x.

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