Prony approximation for f( x) fits an exponential sum S n(x) ≏ ∑ i=1 n A ie αix to m values f( x j ), m ≥ 2 n, j = 0(1) m − 1, for x j 's equally-spaced at intervals of h. The α i 's are obtained from e α i h , the roots of an n th degree algebraic equation whose coefficients are found from the f( x j )'s. For nodes x j spaced unequally, there is neither a Prony approximation, nor, for interpolation, an exponential analogue of divided differences of tabulated functions. But when all the nodes x j coalesce to x 0, there is a confluent Prony approximation (CPA), where S n (j)(x 0) ⋟ tf (j)(x 0), j = 0(1)m − 1 . Here the α i 's themselves are the roots of an equation whose coefficients are found similarly, but from the f ( j) ( x 0)'s. CPA obtains exponential terms in S n ( x) that would be undetectable at nodes x j away from χ 0. For m = 2 n, CPA becomes interpolation that is equivalent to Gaussian quadrature for I( x) ≡ ∫ a b w( t) e xt dt, where w( t), a and b depend upon f( x), the moments being f ( j) ( x 0), j = 0(1)2 n − 1. In tests on three different f( x)′ s, CPA converged better than the Taylor series at x 0. Numerical integration of differential equations involving functions of an exponential nature may employ CPA for predictors in conjunction with Obreschkoff formulas for correctors.