Weierstrass Product Inequality

Author

Eric W. Weisstein
April 15, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/WeierstrassProductInequality.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/WeierstrassProductInequality.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Four Variables

FindInstance[(1-a)(1-b)(1-c)(1-d)+a+b+c+d<1&&
0≤a≤1&&
0≤b≤1&&
0≤c≤1&&
0≤d≤1,
{a,b,c,d}]

Arbitrary Number of Variables

WeierstrassProductInequality[l_List]:=Times@@((1-#)&/@l)+Plus@@l<1&&And@@(0≤#≤1&/@l)

WeierstrassProductInequality[{a,b}]//TraditionalForm

WeierstrassProductInequality[{a,b,c,d}]//TraditionalForm

Table[FindInstance[WeierstrassProductInequality[l=Array[a,n]],l],
{n,5}]//Timing

Induction Proof

Factor[(1-z)p-p+z]