TRANSCENDENCE AND ALGEBRAIC INDEPENDENCE OF THE VALUES OF SOME HYPERGEOMETRIC $ E$-FUNCTIONS
I. I. Belogrivov · Mathematics of the USSR-Sbornik · 1970
We investigate the arithmetical character of the values of the functions where , are rational numbers; , , , are arbitrary nonnegative rational integers, , , ; , , , , , a natural number. The function is the solution of a linear differential equation of order with polynomial coefficients. The system of functions , , constitutes the solution of a system of linear differential equations whose coefficients are rational functions of . By means of the general theorem of Šidlovskiĭ on the transcendence and algebraic independence of the values of the -functions we prove six theorems on the mutual transcendence of the values of the functions in each aggregate and , at arbitrary algebraic points for various rational values of the parameters , and arbitrary values . Bibliography: 8 items.