complex%20variables
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1: 6.19 Tables
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§6.19(ii) Real Variables
… ►Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
§6.19(iii) Complex Variables,
►Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of , , , 6D; , , , 6D; , , , 6D.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of , , , 8S.
2: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Several Complex Variables.
Princeton Mathematical Series, Vol. 10, Princeton University Press, Princeton, N.J..
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3: 22.3 Graphics
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§22.3(i) Real Variables: Line Graphs
… ►§22.3(ii) Real Variables: Surfaces
… ►§22.3(iii) Complex ; Real
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…4: 15.10 Hypergeometric Differential Equation
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15.10.1
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15.10.3
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15.10.5
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15.10.7
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►The connection formulas for the principal branches of Kummer’s solutions are:
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5: 25.11 Hurwitz Zeta Function
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has a meromorphic continuation in the -plane, its only singularity in being a simple pole at with residue .
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25.11.2
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25.11.3
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25.11.42
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6: 5.22 Tables
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►For early tables for both real and complex variables see Fletcher et al. (1962), Lebedev and Fedorova (1960), and Luke (1975, p. 21).
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§5.22(ii) Real Variables
►Abramowitz and Stegun (1964, Chapter 6) tabulates , , , and for to 10D; and for to 10D; , , , , , , , and for to 8–11S; for to 20S. … ►§5.22(iii) Complex Variables
…7: 9.18 Tables
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§9.18(ii) Real Variables
… ►Zhang and Jin (1996, p. 337) tabulates , , , for to 8S and for to 9D.
§9.18(iii) Complex Variables
… ►Sherry (1959) tabulates , , , , ; 20S.
8: 25.12 Polylogarithms
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►In the complex plane has a branch point at .
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►For real or complex
and the polylogarithm
is defined by
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►For each fixed complex
the series defines an analytic function of for .
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9: 7.23 Tables
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§7.23(ii) Real Variables
… ►§7.23(iii) Complex Variables,
… ►Zhang and Jin (1996, pp. 638, 640–641) includes the real and imaginary parts of , , , 7D and 8D, respectively; the real and imaginary parts of , , , 8D, together with the corresponding modulus and phase to 8D and 6D (degrees), respectively.
10: 30.9 Asymptotic Approximations and Expansions
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►For uniform asymptotic expansions in terms of Airy or Bessel functions for real values of the parameters, complex values of the variable, and with explicit error bounds see Dunster (1986).
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►For uniform asymptotic expansions in terms of elementary, Airy, or Bessel functions for real values of the parameters, complex values of the variable, and with explicit error bounds see Dunster (1992, 1995).
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►The behavior of for complex
and large is investigated in Hunter and Guerrieri (1982).
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