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1: 1.14 Integral Transforms
§1.14 Integral Transforms
where the last integral denotes the Cauchy principal value (1.4.25). … If f ( t ) is absolutely integrable on [ 0 , R ] for every finite R , and the integral (1.14.47) converges, then …
§1.14(viii) Compendia
For more extensive tables of the integral transforms of this section and tables of other integral transforms, see Erdélyi et al. (1954a, b), Gradshteyn and Ryzhik (2000), Marichev (1983), Oberhettinger (1972, 1974, 1990), Oberhettinger and Badii (1973), Oberhettinger and Higgins (1961), Prudnikov et al. (1986a, b, 1990, 1992a, 1992b).
2: Sidebar 22.SB1: Decay of a Soliton in a Bose–Einstein Condensate
Sidebar 22.SB1: Decay of a Soliton in a BoseEinstein Condensate
Among these are the formation of vortex rings in Bose Einstein condensates. …For details see the NIST news item Decay of a dark soliton into vortex rings in a BoseEinstein condensate. … Cornell, Watching Dark Solitons Decay into Vortex Rings in a BoseEinstein Condensate, Phys. Rev. Lett. 86, 2926–2929 (2001)
3: 25.17 Physical Applications
See Armitage (1989), Berry and Keating (1998, 1999), Keating (1993, 1999), and Sarnak (1999). The zeta function arises in the calculation of the partition function of ideal quantum gases (both BoseEinstein and Fermi–Dirac cases), and it determines the critical gas temperature and density for the BoseEinstein condensation phase transition in a dilute gas (Lifshitz and Pitaevskiĭ (1980)). …
4: 8.19 Generalized Exponential Integral
§8.19 Generalized Exponential Integral
§8.19(i) Definition and Integral Representations
Other Integral Representations
§8.19(ii) Graphics
§8.19(x) Integrals
5: 29.19 Physical Applications
Bronski et al. (2001) uses Lamé functions in the theory of BoseEinstein condensates. …
6: 6.2 Definitions and Interrelations
§6.2(i) Exponential and Logarithmic Integrals
The logarithmic integral is defined by …
§6.2(ii) Sine and Cosine Integrals
7: 25.18 Methods of Computation
For dilogarithms and polylogarithms see Jacobs and Lambert (1972), Osácar et al. (1995), Spanier and Oldham (1987, pp. 231–232), and Zudilin (2007). For Fermi–Dirac and BoseEinstein integrals see Cloutman (1989), Gautschi (1993), Mohankumar and Natarajan (1997), Natarajan and Mohankumar (1993), Paszkowski (1988, 1991), Pichon (1989), and Sagar (1991a, b). …
8: 8.21 Generalized Sine and Cosine Integrals
§8.21 Generalized Sine and Cosine Integrals
§8.21(iii) Integral Representations
§8.21(iv) Interrelations
§8.21(v) Special Values
9: 25.12 Polylogarithms
The right-hand side is called Clausen’s integral. …
Integral Representation
§25.12(iii) Fermi–Dirac and BoseEinstein Integrals
The Fermi–Dirac and BoseEinstein integrals are defined by … In terms of polylogarithms …
10: 7.2 Definitions
§7.2(ii) Dawson’s Integral
§7.2(iii) Fresnel Integrals
Values at Infinity
§7.2(iv) Auxiliary Functions
§7.2(v) Goodwin–Staton Integral