#C13.txt: March 1, 2018, ExpMath (RU) Help:=proc(): print(` H(s) , Z(u) , It(t,D1), Jt(t,D1), CheckP58L10() `):end: #H(s): (15.3) H:=proc(s): evalf(1/2*s*(1-s)*Pi^(-s/2)*GAMMA(s/2)): end: Z:=proc(u) Re(evalf(H(1/2+I*u)/abs(H(1/2+I*u))*Zeta(1/2+I*u))): end: #It(t,D1): Int(Z(u),u=t..t+D1):(15.5) It:=proc(t,D1): evalf(Int(Z(u),u=t..t+D1)): end: #Jt(t,D1): Int(abs(Z(u)),u=t..t+D1):(15.6) Jt:=proc(t,D1): evalf(Int(abs(Z(u)),u=t..t+D1)): end: #CheckP58L10(): checks Line 10 p. 58 of Iwaniec's book CheckP58L10:=proc(n,t,D1) local u: int(n^(-1/2-I*u),u=t..t+D1): end: