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Bose–Einstein integrals

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1: 25.12 Polylogarithms
§25.12(iii) Fermi–Dirac and BoseEinstein Integrals
The Fermi--Dirac and Bose--Einstein integrals are defined by …
25.12.15 G s ( x ) = 1 Γ ( s + 1 ) 0 t s e t - x - 1 d t , s > - 1 , x < 0 ; or s > 0 , x 0 ,
In terms of polylogarithms …
G s ( x ) = Li s + 1 ( e x ) .
2: 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). …
3: 25.21 Software
§25.21(vii) Fermi–Dirac and BoseEinstein Integrals
4: Bibliography G
  • W. Gautschi (1993) On the computation of generalized Fermi-Dirac and Bose-Einstein integrals. Comput. Phys. Comm. 74 (2), pp. 233–238.
  • 5: Bibliography D
  • R. B. Dingle (1957a) The Bose-Einstein integrals p ( η ) = ( p ! ) - 1 0 ϵ p ( e ϵ - η - 1 ) - 1 d ϵ . Appl. Sci. Res. B. 6, pp. 240–244.
  • 6: Software Index
    7: Bibliography B
  • G. E. Barr (1968) A note on integrals involving parabolic cylinder functions. SIAM J. Appl. Math. 16 (1), pp. 71–74.
  • W. Bartky (1938) Numerical calculation of a generalized complete elliptic integral. Rev. Mod. Phys. 10, pp. 264–269.
  • P. A. Becker (1997) Normalization integrals of orthogonal Heun functions. J. Math. Phys. 38 (7), pp. 3692–3699.
  • J. C. Bronski, L. D. Carr, B. Deconinck, J. N. Kutz, and K. Promislow (2001) Stability of repulsive Bose-Einstein condensates in a periodic potential. Phys. Rev. E (3) 63 (036612), pp. 1–11.
  • P. J. Bushell (1987) On a generalization of Barton’s integral and related integrals of complete elliptic integrals. Math. Proc. Cambridge Philos. Soc. 101 (1), pp. 1–5.