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Content

Complex Functions

plane curve in real domain

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

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

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

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)

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

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

2D surface in complex domain

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

    3D in complex domain

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

Complex

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

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• Math - Symbol - Handbook - math word
• Elementary Math - Higher Math
• Calculator - mathHand - mathHandbook
• Function - Formula - equation - graphics
• Fractional Calculus - differential equation
• Example :

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