#C14.txt, March 5, 2018, ExpMath (Rutgers University) Help:=proc(): print(` H(s), LogHs(s) , Y(g,s), xi(s), G(g,s), Check174(g,s0) , Check187(s0,m), Check188(s0,j,T) `): end: H:=proc(s) 1/2*s*(1-s)*Pi^(-s/2)*GAMMA(s/2): end: xi:=proc(s) H(s)*Zeta(s): end: #LogHs(s): the log. der. of H(s), H'(s)/H(s) LogHs:=proc(s) diff(H(s),s)/H(s): end: Y:=proc(g,s) local edna: edna:=LogHs(s): 2-g*(edna+subs(s=1-s,edna)): end: G:=proc(g,s) Zeta(s)+g*diff(Zeta(s),s):end: #Check174(g,s0): checks Eq. (17.4) with G(s) and Y(s) given by (17.5) and (17.6) Check174:=proc(g,s0) local s,amit: amit:=Y(g,s)*xi(s)-H(s)*G(g,s)-subs(s=1-s,H(s)*G(g,s)): evalf(subs(s=s0,amit)): end: #Check187(s,m): the left side of (18.7) divided by the right side for any s=s0 and m Check187:=proc(s0,m) local ra: ra:=diff(H(s),s$m)/H(s)/(1/2*log(s/2/Pi))^m: evalf(subs(s=s0,ra)): end: #Check188(s0,j,T): checks (18.8) Check188:=proc(s0,j,T) local anthony,s,n: anthony:=diff(Zeta(s),s$j)-add((-log(n))^j*n^(-s),n=1..T): evalf(subs(s=s0,anthony)*T^(1/4)): end: