|
MathGrapher | The Mathematical Graphing Tool for Students, Scientists and Engineers
 
 
 

Modules

  • Functions
  •    =>
  • Data
  • Curve Fitting
  • Iterations
  • ODEs
  • Matrices
  • L-systems
  • Game of life
  • Screenviews
  • Functions, 2D and 3D Functions in 2D and 3D
    You are here: Modules > Functions
    Links in the text refer to the lower part of the page

    Functions in 2D and 3D

    Functions of the form F(x) and F(x,y) containing up to 20 subfunctions, 30 special functions, 150 numerical and 100 named constants.

    Special Functions

    Special Functions (real numbers only!)


    Random numbers


    Modulo function


    Fresnel integrals:


    Exponential integrals and related functions


    Gamma function and related functions


    Riemann Zeta function


    Bessel functions


    Elliptic integrals


    Airy functions


    Probability function


    Distribution functions

    Special functions: Riemann Zeta function
    Riemann Zeta function: Zeta(x)

                 

           This series is convergent for all numbers s>1. This holds
    for all complex numbers with real part >1.
    Euler showed that it is connected with the prime numbers
    by the relation

                 

           where the product runs over all prime numbers p.
     
    Riemann found an analytical continuation to this function
    for all s except 1

                 

           The integral runs from infinity to zero just above the real
    axis, turns aorund zero and runs back to infinity just below the real axis
    Mathgrapher calculates this function along the real axis (s=1 excluded)

     
    The famous Riemann hypothesis states that all
    (non-trivial) zeroes of this function are on the line Re(s)=1/2.
    This Riemann hypothesis is unproved although more than
    10^13 zeroes have been found, all of which ly on this line.

          

          

          

                  More information

     
     
     
     
     
      © MathGrapher 2006 | Freeware since 25 october 2013   Contact the Webmaster