NIST Handbook of Mathematical Functions

By F. Olver, D. Lozier, R. Boisvert, Charles W. Clark. 2010

5,017 citations recorded by the source corpus.

Subfields: Numerical Methods & Scientific Computing

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In Numerical Methods & Scientific Computing

Citations in the corpus

Hopular: Modern Hopfield Networks for Tabular Data (2022, neutral): “We define a := 2/d−1(1+ln(2βK2p(d−1))), b := 2K2β/5, and c := b/W0(exp(a+ln(b)), where W0 is the upper branch of the Lambert W function (Olver et al., 2010, (4.13)), and ensure c ≥ (2/√p)4/d−1.”
Acoustic inverse scattering using topological derivative of far-field measurements-based L2 cost functionals (2013, neutral): “In practice, numerical experiments on other, more complex problems [27] indicate that the number of sources and observations can be substantially reduced while inducing only moderate degradations on the reconstructions.”
Multiplicity-induced-dominancy for delay-differential equations of retarded type (2020, methodology): “As presented in [13,20,39], the function M ( a, b, · ) satisﬁes Kummer’s diﬀerential equation Other solutions of (2.4) are usually also called Kummer’s conﬂuent hypergeometric functions, but they shall not be used in this paper.”
Inequalities for modified Bessel functions and their integrals (2012, neutral): “[13] we have, for ν = −1/2, ∫ zLν(z) dz = √ π2ν−1Γ (ν + 1/2)z ( Lν(z)Lν−1(z)−Lν−1(z)Lν(z) ) .”
Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations (2015, neutral): “Applying Stirling’s approximation [48] √ we obtain (2.12) ( We also have Combining (2.13), (2.14) with the Leibniz rule, we obtain (2.18) Proof .”
Short-time near-the-money skew in rough fractional volatility models (2017, background): “where 2F1 denotes the Gaussian hypergeometric function [Olv10].”
A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain (2011, neutral): “From a numerical perspective, the continued fraction expansion for H (a, z) is particularly convenient to use (cf. Olver et al. 2010, eqn (8.9.1)) H (a, z) = e−z · 1 a − az a + 1 + z a + 2 − (a + 1)z a + 3 + 2z a + 4 − (a + 2)z a + 5 + 3z a + 6 − · · · .”
Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles (2014, background): “In Section 6, we show that the model indeed has the predicted non-perturbative saddle points, the unitons and fractons, and describe their properties.”