prodeuler

Function: prodeuler
Section: sums
C-Name: prodeuler0
Prototype: V=GGEp
Help: prodeuler(p=a,b,expr): Euler product (p runs over the primes between a
 and b) of real or complex expression, as a floating point approximation.
Doc: product of expression \var{expr}, initialized at \kbd{1.0}
 (i.e.~to a floating point number equal to 1 to the
 current \kbd{realprecision}), the formal parameter $p$ ranging over the prime
 numbers between $a$ and $b$.\sidx{Euler product}
 \bprog
 ? prodeuler(p = 2, 10^4, 1 - p^-2)
 %1 = 0.60793306911405513018380499671124428015
 ? P = 1; forprime(p = 2, 10^4, P *= (1 - p^-2))
 ? exponent(numerator(P))
 %3 = 22953
 @eprog\noindent The function returns a floating point number because,
 as the second expression shows, such products are usually intractably
 large rational numbers when computed symbolically.
 If the expression is a rational funtction, \kbd{prodeulerrat} computes the
 product over all primes:
 \bprog
 ? prodeulerrat(1 - p^-2)
 %4 = 0.60792710185402662866327677925836583343
 ? 6/Pi^2
 %3 = 0.60792710185402662866327677925836583343
 @eprog

 \synt{prodeuler}{void *E, GEN (*eval)(void*,GEN), GEN a,GEN b, long prec}.