exponential%20function
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11: 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
… ►For corresponding results for argument derivatives of the theta functions see Erdélyi et al. (1954a, pp. 224–225) or Oberhettinger and Badii (1973, p. 193). …12: 26.12 Plane Partitions
13: Bibliography G
14: 11.14 Tables
§11.14(ii) Struve Functions
… ►Agrest et al. (1982) tabulates and for and to 11D.
Zhang and Jin (1996) tabulates and for and to 8D or 7S.
§11.14(iv) Anger–Weber Functions
… ►§11.14(v) Incomplete Functions
…15: 10.73 Physical Applications
§10.73(iii) Kelvin Functions
… ►§10.73(iv) Bickley Functions
…16: 25.5 Integral Representations
§25.5 Integral Representations
►§25.5(i) In Terms of Elementary Functions
… ►§25.5(ii) In Terms of Other Functions
… ►For similar representations involving other theta functions see Erdélyi et al. (1954a, p. 339). … ►§25.5(iii) Contour Integrals
…17: 6.19 Tables
§6.19(ii) Real Variables
►Abramowitz and Stegun (1964, Chapter 5) includes , , , , ; , , , , ; , , , , ; , , , , ; , , . Accuracy varies but is within the range 8S–11S.
Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
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.
18: 7.8 Inequalities
19: 12.19 Tables
§12.19 Tables
… ►Miller (1955) includes , , and reduced derivatives for , , 8D or 8S. Modulus and phase functions, and also other auxiliary functions are tabulated.
Fox (1960) includes modulus and phase functions for and , and several auxiliary functions for , , 8S.
Karpov and Čistova (1968) includes and for and = 0(.001 or .0001)5, , 7D or 8S.
Murzewski and Sowa (1972) includes for , , 7S.