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Example of Graphics

Complex function in real domain

Content

Complex Functions

plane curve in real domain

plot with re2D(x) for 2 curves of real and imag values. First curve is real value, second curve is imag value.
  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
  10. Img value of Circular and Hyperbolic functions in real domain are 0. So only their inverse functions are shown :

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

plane curve in imag domain

plot with im2D(x) for 2 curves of real and imag values. First curve is real value, second curve is imag value.
  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)
  10. real value of Circular and Hyperbolic functions in imag domain are 0. So only their inverse functions are shown :

  11. Circular sine
  12. Circular cosine
  13. Circular tangent
  14. Circular cotangent
  15. Circular secant
  16. Circular cosecant
  17. Hyperbolic sine
  18. Hyperbolic cosine
  19. Hyperbolic tangent
  20. Hyperbolic cotangent
  21. Hyperbolic secant
  22. Hyperbolic cosecant
  23. Bessel function of first kind
  24. Bessel function of second kind
  25. Modified Bessel function of first kind
  26. Modified Bessel function of second kind
  27. Hankel function of first kind
  28. Hankel function of second kind
  29. Airy function of first kind
  30. Airy function of second kind
  31. Elliptic integral of first kind
  32. Elliptic integral of second kind
  33. Elliptic integral of third kind
  34. Jacobi zeta function
  35. Jacobi elliptic sine
  36. Jacobi elliptic cosine
  37. Jacobi delta amplitude
  38. Jacobi amplitude
  39. Weierstrass elliptic function
  40. Gamma function
  41. Logarithm of gamma function
  42. Riemann zeta function
  43. 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

complex - complex math
  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

See Also

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