In mathematics, the Stieltjes transformation Sρ(z) of a measure of density ρ on a real interval I is the function of the complex variable z defined outside...

Riemann–Stieltjes integral Stieltjes constants Stieltjes matrix Stieltjes moment problem Stieltjes polynomials Stieltjes transformation (and Stieltjes inversion...

the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition...

transform Poisson–Mellin–Newton cycle N-transform Radon transform Stieltjes transformation Sumudu transform Wavelet transform (integral) Weierstrass transform...

}{1-\alpha z}}.} The Cauchy transform (which is the negative of the Stieltjes transformation) is given by G ( z ) = z + α − λ α − ( z − α ( 1 + λ ) ) 2 − 4...

Springer-Verlag, 1971 Analytic hierarchy process Keller's conjecture Stieltjes transformation Scott, W. T. (1955). "Review: Oskar Perron, Die Lehre von den Kettenbrüchen...

probability theory, and in mathematical statistics, the use of the Fourier—Stieltjes transform is preferred, because so many random variables are not of continuous...

{\pi }{2}}.} The (unilateral) Laplace–Stieltjes transform of a function g : ℝ → ℝ is defined by the Lebesgue–Stieltjes integral { L ∗ g } ( s ) = ∫ 0 ∞ e...

called the reducer of ρ. More generally, μ et ρ are linked by their Stieltjes transformation with the following formula: S μ ( z ) = z − c 1 − 1 S ρ ( z ) {\displaystyle...

recovered from N by employing the Stieltjes inversion formula (related to the inversion formula for the Stieltjes transformation): μ ( ( λ 1 , λ 2 ] ) = lim...