Approximation formulas for the constant e and an improvement to a Carleman-type inequality

Abstract

A Ap p pp p pr r ro o ox x xi i im m ma a at t ti i io o on n n f f fo o or r rm m mu u ul l la a as s s f f fo o or r r t t th h he e e c c co o on n ns s st t ta a an n nt t t e e e a a an n nd d d a a an n n i i im m mp p pr r ro o ov v ve e em m me e en n nt t t t t to o o a a a C C Ca a ar r rl l le e em m ma a an n n-t t ty y yp p pe e e i i in n ne e eq q qu u ua a al l li i it t ty y y