Hille–Hardy formula
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11—20 of 264 matching pages
11: Bibliography E
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The Euler-Maclaurin formula revisited.
J. Austral. Math. Soc. Ser. B 40 (E), pp. E27–E76 (electronic).
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Tables of Integral Transforms. Vol. I.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Tables of Integral Transforms. Vol. II.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Higher Transcendental Functions. Vol. II.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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Higher Transcendental Functions. Vol. III.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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12: 28.34 Methods of Computation
13: 28.30 Expansions in Series of Eigenfunctions
14: Brian R. Judd
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►Judd’s books include Operator Techniques in Atomic Spectroscopy, published by McGraw-Hill in 1963 and reprinted by Princeton University Press in 1998, Second
Quantization and Atomic Spectroscopy, published by Johns Hopkins in 1967, Topics in Atomic and Nuclear Theory (with J.
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15: Gerhard Wolf
16: 1.3 Determinants, Linear Operators, and Spectral Expansions
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Krattenthaler’s Formula
… ►Of importance for special functions are infinite determinants of Hill’s type. These have the property that the double series …Hill-type determinants always converge. …17: Bibliography W
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Reduction formulae for products of theta functions.
J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.
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Hill’s equation with a large potential.
SIAM J. Appl. Math. 45 (2), pp. 200–214.
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Asymptotic behavior of stability regions for Hill’s equation.
SIAM J. Appl. Math. 47 (5), pp. 941–958.
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Recursion formulae for hypergeometric functions.
Math. Comp. 22 (102), pp. 363–373.
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Quadrature formulas for oscillatory integral transforms.
Numer. Math. 39 (3), pp. 351–360.
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18: 29.7 Asymptotic Expansions
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►Formulas for additional terms can be computed with the author’s Maple program LA5; see §29.22.
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►Weinstein and Keller (1985) give asymptotics for solutions of Hill’s equation (§28.29(i)) that are applicable to the Lamé equation.
19: 28.32 Mathematical Applications
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