Handbook Of Mathematical Functions

By T. Gerber. 2016

6,714 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6f2718bb53fd422b0698d038eef48266aa8dd0ea

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Citations in the corpus

The scenario approach for Stochastic Model Predictive Control with bounds on closed-loop constraint violations (2013, background): “loits the result of Lemma 12 to obtain an upper bound on the expectation EKN Vt x t := Z ∆KN Vt|xt(Ωt)dP KN . (10) A reformulation via the indicator function 1: ∆KN → {0,1} yields that EKN Vt x t = Z [0,1] Z ∆KN 1 Vt|xt(Ωt) >ν dPKNdν = Z [0,1] PKN Vt|xt(Ωt) >ν dν ≤ Z [0,1] UK,R,ρ1(ν)dν . (11) ”
Optimal Hamiltonian Simulation by Quantum Signal Processing. (2016, methodology): “1 |k|! ∣∣ τ 2 ∣∣|k| [30] decays rapidly with k, good approxima-”
A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm (2015, background): “27 in [51], which reads J′ n(α m ` ) = −Jn+1(α` ) + n αm ` Jn(α` ), and took into account the fact that Jn(α` ) = 0 in our case.”
Metamodel-based sensitivity analysis: polynomial chaos expansions and Gaussian processes (2016, unknown): “rthogonal polynomials fP(i) k ;k2 Ngsatisfying D P(i) j ;P (i) k E i def= E h P(i) j (X i)P (i) k (X i) i = Z D X i P(i) j (x) P (i) k (x) f X i (x)dx= a(i) j jk; (5) see e.g. Abramowitz and Stegun [1]. In the above equation subscript k denotes the degree of the polynomial P(i) k , jkis the Kronec”
Meta‐regression approximations to reduce publication selection bias (2014, background): “Some of these approximations are in fact power series (Abramowitz and Stegun, 1964).”
Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics (2016, background): “, z ∈ R, which is a special case of the generalized hypergeometric functions qFp (Abramowitz and Stegun, 1970), with (q)k = Γ(q+ k)/Γ(q) for k ∈ N∪{0}, being the Pochhammer symbol.”
Seismic Ray Theory (2001, background): “14), H (1) 0 is the Hankel function of the first kind and zeroth-order; see Abramowitz and Stegun (1970).”
On deep learning as a remedy for the curse of dimensionality in nonparametric regression (2019, background): “,q}, j1+···+jd≤q ∥∥∥∥ ∂j1+···+jdf ∂j1x(1) · · · ∂jdx(d) ∥∥∥∥ ∞ ≤ c2, (11)”