The NON-DIAGONAL MATRIX ELEMENTS < g vertical bar r(k) vertical bar g(t) >, < f vertical bar r(k) vertical bar f(t) >, < g vertical bar r(k) | f(t) >, < f vertical bar r(k) vertical bar g(t) >, WITH THE RADIAL FUNCTIONS OF THE DIRAC g(r) AND f(r) FOR ARBITRARY nlj - STATES OF THE 3H-ATOM AND THEIR REPRESENTATION THROUGH THE APPEL FUNCTION F-2(x, y) IN A NEIGHBORHOOD OF A SINGULAR POINT (1,1). SPECTRAL SERIES OF LYMAN AND BALMER (n <= 3, n' <= l +/- 1, k = 1, AND Z = 1, 2, 10, 18, 36, 54, 86, 101, 118) AND GRAPHS OF THE RADIAL FUNCTIONS G(r) = rg, F(r) = rf AND P-nl(r) FOR Z =1, 118, AND 137, n<3

This article deals with the connection between a.m. the off-diagonal matrix elements and new properties of Appell's function F-2(x, y) to the vicinity of the singular point (1,1). Such approach allows to get the exact analytical expressions and numerical values of these elements for arbitrary nlj-states of 3H-like atoms and Z <= 118. Relativistic dipole moments dmD of T. Lyman's (1906-1914) and J. Balmer's (1885) spectral series are compared with the values dmS on the basis of Schrodinger theory (as n <= 3, n' <= l +/- 1, k = 1 and Z = 1, 2, 10, 18, 36, 54, 86, 101, 118) for the first time.