In mathematics, the Stieltjesconstants are the numbers γ k {\displaystyle \gamma _{k}} that occur in the Laurent series expansion of the Riemann zeta...
Riemann–Stieltjes integral StieltjesconstantsStieltjes matrix Stieltjes moment problem Stieltjes polynomials Stieltjes transformation (and Stieltjes inversion...
gamma function, the polygamma functions, the Stieltjesconstants and many other special functions and constants may be expressed in terms of infinite series...
_{n=0}^{\infty }{\frac {\gamma _{n}}{n!}}(1-s)^{n}.} The constants γn here are called the Stieltjesconstants and can be defined by the limit γ n = lim m → ∞ (...
Malmsten's integrals are also found to be closely connected to the Stieltjesconstants. In 1842, Malmsten also evaluated several important logarithmic series...
\atop m+1}\right]\left[{n \atop 2k+1}\right]\,} where γm are the Stieltjesconstants and δm,0 represents the Kronecker delta function. Notice that this...
B_{1}\approx 0.26149721} is the Mertens constant and γ j {\displaystyle \gamma _{j}} are the Stieltjesconstants. The function ω ( n ) {\displaystyle \omega...
products. The Lebesgue–Stieltjes integral is the ordinary Lebesgue integral with respect to a measure known as the Lebesgue–Stieltjes measure, which may be...
"A theorem for the closed-form evaluation of the first generalized Stieltjesconstant at rational arguments and some related summations". Journal of Number...
"A theorem for the closed-form evaluation of the first generalized Stieltjesconstant at rational arguments and some related summations". Journal of Number...
. Kalugin, German A.; Jeffrey, David J.; Corless, Robert M. (2011). "Stieltjes, Poisson and other integral representations for functions of Lambert W"...
between the zeta functions, as well as in various formulas for the Stieltjesconstants, e.g. γ m ( v ) = − ln m + 1 ( v + a ) m + 1 + ∑ n = 0 ∞ ( − 1...
and related branches of mathematics, the Lebesgue–Stieltjes integral generalizes Riemann–Stieltjes and Lebesgue integration, preserving the many advantages...
{\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...
Fourier–Stieltjes transform of its distribution measure, but in this context it is typical to take a different convention for the constants. Typically...
Hermite; letter to Thomas Joannes Stieltjes about Weierstrass functions, Correspondance d'Hermite et de Stieltjes vol.2, p.317-319 In addition to the...
..) is the sequence of moments of some positive Borel measure μ. The Stieltjes moment problem, Vorobyev moment problem, and the Hausdorff moment problem...
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