   An interface for evaluation of Euler sums.
 Implementation details: EZ-Face is based on our fast method for computing Euler sums by turning them into convolutions of geometrically converging nested sums. This method is described in our paper Special values of multiple polylogarithms,'' see the References page. The method was coded in the C language using the GNU MP multiprecision library. EZ-Face has been limited to the precision of 100 digits. A typical computation will complete within few seconds. Syntax: Standard syntax for computer representation of mathematical expressions (as used by Maple) is assumed. The value can be computed by typing in z( s1 , ... , sk ). The value can be computed by typing in zp( p , s1 , ... , sk ). The z() and zp() functions can be used within any Maple expression. Their values are calculated before being passed to Maple. So, the arguments of z or zp are not evaluated and must be non-zero integers (syntactically!), the only exception being the value of p, i.e. the first argument of zp(...), which must be an integer or a floating-point number. The function lindep( [ x1 , ... , xn ] ) can be used to discover a vanishing linear combination (with integer coefficients) of the values x1 , ... , xn. Examples: Input Pi^6 / z(6) evaluates to 945.00000.... ... Instance of Euler's formula for . Input z(3,1,3,1,3,1) - 2 * Pi^12 / 14! evaluates to 0 ... Instance of the now proven Zagier conjecture. Input lindep( [ z(-1,2) , log(2)*Pi^2 , z(3) ] ) evaluates to 12. , -1. , 3. ... Discovery of the relation .

[ Main page | Definitions | Using EZ-Face | References | Credits ]