Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)

By M. Abramowitz, I. Stegun, R. H. Romer. 1965

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Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering (2015, methodology): “We use the Mehler formula for w such that 2w 1−w2 = 1 τ2 (Abramowitz and Stegun, 2012):”
Gaussian Process Regression Networks (2011, background): “Indeed the OU kernel belongs to a more general class of Mat´ern kernels, where K α is a modiﬁed Bessel function (Abramowitz and Stegun, 1964).”
Hierarchical matrix techniques for low- and high-frequency Helmholtz problems (2007, unknown): “Since according to equation (9.1.60) in Abramowitz & Stegun (1992), Jm(ρ) 6 √ 1/2 and ∣ ∣ 1 π ∫ π 0 sin(ρ sinθ − mθ)dθ ∣ ∣ 6 1π ∫ π 0 dθ = 1, we have that |Hm(ρ)| 6 √ 3/2 + 2 π ∫ ∞ 0 emt−ρ sinht dt.”
The cosmological bootstrap: inflationary correlators from symmetries and singularities (2018, unknown): “The following formulas relate hypergeometric functions at different values of the argument [150]:”
Quantum extremal islands made easy. Part II. Black holes on the brane (2020, unknown): “25) of [109].”
Quantum supremacy of many-particle thermal machines (2015, background): “in terms of the standard polylogarithm function Lin(z) = ∑j=1 j−nz j, n ≥ 1 [46].”
Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions (2013, methodology): “The Chebyshev inclusion function is mainly used to evaluate the coefficients of polynomials, which can be implemented via numerical integrals with respect to uncertain parameters, for example, the Mehler integral (or called Gaussian–Chebyshev integral formula [33]).”