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    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.




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