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1: 20.10 Integrals
§20.10 Integrals
►§20.10(i) Mellin Transforms with respect to the Lattice Parameter
… ►Here again denotes the Riemann zeta function (§25.2). … ►§20.10(ii) Laplace Transforms with respect to the Lattice Parameter
… ►Then …2: 25.11 Hurwitz Zeta Function
§25.11 Hurwitz Zeta Function
►§25.11(i) Definition
… ►The Riemann zeta function is a special case: … ►§25.11(xii) -Asymptotic Behavior
… ►Similarly, as in the sector , …3: 20.7 Identities
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§20.7(v) Watson’s Identities
… ►§20.7(vi) Landen Transformations
… ►§20.7(vii) Derivatives of Ratios of Theta Functions
… ►See Lawden (1989, pp. 19–20). … ►§20.7(viii) Transformations of Lattice Parameter
…4: 15.10 Hypergeometric Differential Equation
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Singularity
… ►Singularity
… ►Singularity
… ►(c) If the parameter in the differential equation equals , then fundamental solutions in the neighborhood of are given by times those in (a) and (b), with and replaced throughout by and , respectively. … ►The connection formulas for the principal branches of Kummer’s solutions are: …5: Bibliography D
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for prolate spheroidal functions with large parameters.
SIAM J. Math. Anal. 17 (6), pp. 1495–1524.
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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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Conical functions with one or both parameters large.
Proc. Roy. Soc. Edinburgh Sect. A 119 (3-4), pp. 311–327.
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Uniform asymptotic expansions for oblate spheroidal functions I: Positive separation parameter
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Proc. Roy. Soc. Edinburgh Sect. A 121 (3-4), pp. 303–320.
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6: Bibliography N
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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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Coulomb Functions for Large Values of the Parameter
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Technical report
Atomic Energy of Canada Limited, Chalk
River, Ontario.
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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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Hypergeometric functions.
Acta Math. 94, pp. 289–349.
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