QRS Constant

Author

Eric W. Weisstein
September 21, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/QRSConstant.nb.

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

©2007 Wolfram Research, Inc. except for portions noted otherwise

(Subscript[C, 1])

Plot[Zeta[1/2,z/2],{z,0,2}]

FindRoot[Zeta[1/2,z/2]==0,{z,.6,0,2},WorkingPrecision->100]

Solve[Zeta[1/2,z/2]==0,z]

FunctionExpand[Zeta[1/2,z/2]]

Transcendental Root

V7

Reduce[Zeta[1/2,z/2]==0&&0<z<2,z,Reals]

C

c1=z/.FindRoot[Zeta[1/2,z/2]==0,{z,.6,0,2},WorkingPrecision->250]

CC=(1/4)Zeta[(3/2),(c1/2)]

CC=(1/4)Zeta[(3/2),(1/2)Root[{Zeta[(1/2),((#1)/2)]&,0.6054436571967327494789228424472080882318462717927597834928`30.102999566398122}]]

N[%,100]