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We give the definition, main properties and integral expressions of the auxiliary function of Riemann R (s). For example we prove ^-s/2 (s/2) R (s) =-e^- i s/4 s-₁^-1+i ^s/2₃' () \, d. Many of these results are known, but they serve as a reference. We give the values of R (s) at integers except at odd natural numbers. We have (12+it) =e^-i (t) Z (t), R (12+it) =12e^-i (t) (Z (t) +iY (t) ), with (t), Z (t) and Y (t) real functions.
Juan Arias de Reyna (Tue,) studied this question.
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