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21—30 of 33 matching pages
21: Bibliography L
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On the Zeros of the Derivative of Bessel Functions of Second Kind.
Pubblicazioni Serie III [Publication Series III], Vol. 179, Istituto per le Applicazioni del Calcolo “Mauro Picone” (IAC), Rome.
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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An efficient derivative-free method for solving nonlinear equations.
ACM Trans. Math. Software 11 (3), pp. 250–262.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Two index laws for fractional integrals and derivatives.
J. Austral. Math. Soc. 14, pp. 385–410.
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22: Bibliography I
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The zeros of regular Coulomb wave functions and of their derivatives.
Math. Comp. 29, pp. 878–887.
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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23: 18.39 Applications in the Physical Sciences
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►Here the term represents the quantum kinetic energy of a single particle of mass , and its potential energy.
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18.39.8
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18.39.38
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18.39.39
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►Derivations of (18.39.42) appear in Bethe and Salpeter (1957, pp. 12–20), and Pauling and Wilson (1985, Chapter V and Appendix VII), where the derivations are based on (18.39.36), and is also the notation of Piela (2014, §4.7), typifying the common use of the associated Coulomb–Laguerre polynomials in theoretical quantum chemistry.
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24: 20.10 Integrals
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►For corresponding results for argument derivatives of the theta functions see Erdélyi et al. (1954a, pp. 224–225) or Oberhettinger and Badii (1973, p. 193).
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25: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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The Riemann zeta-function and its derivatives.
Proc. Roy. Soc. London Ser. A 450, pp. 477–499.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Molecular collisions and cusp catastrophes: Three methods for the calculation of Pearcey’s integral and its derivatives.
Chem. Phys. Lett. 81 (2), pp. 306–310.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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26: 20.11 Generalizations and Analogs
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►Such sets of twelve equations include derivatives, differential equations, bisection relations, duplication relations, addition formulas (including new ones for theta functions), and pseudo-addition formulas.
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27: 18.40 Methods of Computation
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►Results of low ( to decimal digits) precision for are easily obtained for to .
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►Results similar to these appear in Langhoff et al. (1976) in methods developed for physics applications, and which includes treatments of systems with discontinuities in , using what is referred to as the Stieltjes derivative which may be traced back to Stieltjes, as discussed by Deltour (1968, Eq. 12).
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Derivative Rule Approach
►An alternate, and highly efficient, approach follows from the derivative rule conjecture, see Yamani and Reinhardt (1975), and references therein, namely that … ►Comparisons of the precisions of Lagrange and PWCF interpolations to obtain the derivatives, are shown in Figure 18.40.2. …28: Bibliography W
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The zeros of Euler’s psi function and its derivatives.
J. Math. Anal. Appl. 332 (1), pp. 607–616.
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Rapid approximation to the Voigt/Faddeeva function and its derivatives.
J. Quant. Spect. and Rad. Transfer 62 (1), pp. 29–48.
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29: 25.6 Integer Arguments
30: Bibliography D
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Complex zeros of linear combinations of spherical Bessel functions and their derivatives.
SIAM J. Math. Anal. 4 (1), pp. 128–133.
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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