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Content

Complex Functions

plane curve in real domain

1. re(pow(x,x) ) real value in real domain
2. im(pow(x,x) ) imag value in real domain
3. re2D(pow(x,x)) real and imag value in real domain

4. re(sqrt(x)) real value in real domain
5. im(sqrt(x)) imag value in real domain
6. re2D(sqrt(x)) real and imag value in real domain

7. for cbrt(x), input root(x,3)
8. Exponential function
9. Natural logarithm

Img value of Circular and Hyperbolic functions in real domain are 0. So only their inverse functions are shown :

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

plane curve in imag domain

1. re(sqrt(i*x)) real value in imag domain
2. im(sqrt(i*x)) imag value in imag domain
3. im2D(sqrt(x)) real and imag value in imag domain

4. for cbrt(x), input root(x,3)
5. im2D(x^x)

6. re(exp(i*x)) real value in imag domain
7. im(exp(i*x)) imag value in imag domain
8. im2D(exp(x)) real and imag value in imag domain

9. Natural logarithm log(x)

real value of Circular and Hyperbolic functions in imag domain are 0. So only their inverse functions are shown :

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

2D surface in complex domain

1. complexplot(z) surface 2D
2. plotcomplex(z) surface 2D
3. WebXR surface 2D

   3D in real, imag and complex domain

4. plot complex function with complex3D(sqrt(x)) in real, imag and complex domain.

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

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