Abel%20means
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21: Need Help?
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Graphics
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How can I view ‘VRML’? What is it? See Viewing DLMF Interactive 3D Graphics.
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What do the colors mean? See About Color Map.
22: 36 Integrals with Coalescing Saddles
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23: Gergő Nemes
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►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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24: Wolter Groenevelt
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►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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25: 33.24 Tables
26: Bibliography D
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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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The computation of lattice frequency distribution functions by means of continued fractions.
Physica 39 (3), pp. 413–423.
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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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27: 26.12 Plane Partitions
28: 19.22 Quadratic Transformations
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§19.22(ii) Gauss’s Arithmetic-Geometric Mean (AGM)
►The AGM, , of two positive numbers and is defined in §19.8(i). … ►
19.22.8
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19.22.9
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►As , and converge quadratically to and 0, respectively, and converges to 0 faster than quadratically.
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29: 8.25 Methods of Computation
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►See Allasia and Besenghi (1987b) for the numerical computation of from (8.6.4) by means of the trapezoidal rule.
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►The computation of and by means of continued fractions is described in Jones and Thron (1985) and Gautschi (1979b, §§4.3, 5).
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