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Modules

Functions, 2D and 3D Functions in 2D and 3D
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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.