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11—20 of 391 matching pages
11: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Special value of the hypergeometric function and connection formulae among asymptotic expansions.
J. Indian Math. Soc. (N.S.) 51, pp. 161–221.
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12: Bibliography N
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On simplified asymptotic formulas for a class of Mathieu functions.
SIAM J. Math. Anal. 15 (6), pp. 1205–1213.
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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On the large argument asymptotics of the Lommel function via Stieltjes transforms.
Asymptot. Anal. 91 (3-4), pp. 265–281.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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13: 20.11 Generalizations and Analogs
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►As in §20.11(ii), the modulus of elliptic integrals (§19.2(ii)), Jacobian elliptic functions (§22.2), and Weierstrass elliptic functions (§23.6(ii)) can be expanded in -series via (20.9.1).
However, in this case is no longer regarded as an independent complex variable within the unit circle, because is related to the variable of the theta functions via (20.9.2).
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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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14: William P. Reinhardt
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►This is closely connected with his interests in classical dynamical “chaos,” an area where he coauthored a book, Chaos in atomic physics with Reinhold Blümel.
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►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
15: 22.18 Mathematical Applications
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§22.18(i) Lengths and Parametrization of Plane Curves
… ►§22.18(iii) Uniformization and Other Parametrizations
… ► … ►The existence of this group structure is connected to the Jacobian elliptic functions via the differential equation (22.13.1). …16: 36.5 Stokes Sets
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►The Stokes set is itself a cusped curve, connected to the cusp of the bifurcation set:
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►They generate a pair of cusp-edged sheets connected to the cusped sheets of the swallowtail bifurcation set (§36.4).
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►This consists of a cusp-edged sheet connected to the cusp-edged sheet of the bifurcation set and intersecting the smooth sheet of the bifurcation set.
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►This part of the Stokes set connects two complex saddles.
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►In Figure 36.5.4 the part of the Stokes surface inside the bifurcation set connects two complex saddles.
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17: 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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18: 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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19: 25.12 Polylogarithms
20: 17.19 Software
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►Citations in the bulleted list refer to papers for which research software has been made available and can be downloaded via the Web.
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