Some Infinite Integrals and Related Continued Fractions

Let     F ( z , n )= ∫ ^∞ ₀ e^-xz M_x (x) dx,

where the function M_x(x)* is such that the above integral is convergent and that as x ⃗ ∞, M_x (x) e ^-xz ⃗ 0, for all integral values of n ≥ 1 (a condition satisfied in the case of the several functions which were obtained as particular cases of the general M -function).