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Mellin–Barnes integrals

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1: 5.19 Mathematical Applications
§5.19(ii) MellinBarnes Integrals
Many special functions f ( z ) can be represented as a MellinBarnes integral, that is, an integral of a product of gamma functions, reciprocals of gamma functions, and a power of z , the integration contour being doubly-infinite and eventually parallel to the imaginary axis at both ends. …
2: Richard B. Paris
 Wood), published by Longman Scientific and Technical in 1986, and Asymptotics and Mellin-Barnes Integrals (with D. …
3: 8.6 Integral Representations
MellinBarnes Integrals
8.6.10 γ ( a , z ) = 1 2 π i c - i c + i Γ ( s ) a - s z a - s d s , | ph z | < 1 2 π , a 0 , - 1 , - 2 , ,
8.6.12 Γ ( a , z ) = - z a - 1 e - z Γ ( 1 - a ) 1 2 π i c - i c + i Γ ( s + 1 - a ) π z - s sin ( π s ) d s , | ph z | < 3 2 π , a 1 , 2 , 3 , .
4: 7.7 Integral Representations
MellinBarnes Integrals
5: 35.8 Generalized Hypergeometric Functions of Matrix Argument
§35.8(v) MellinBarnes Integrals
Multidimensional MellinBarnes integrals are established in Ding et al. (1996) for the functions F q p and F p p + 1 of matrix argument. …These multidimensional integrals reduce to the classical MellinBarnes integrals5.19(ii)) in the special case m = 1 . …
6: 12.5 Integral Representations
§12.5(iii) MellinBarnes Integrals
7: Bibliography P
  • R. B. Paris and D. Kaminski (2001) Asymptotics and Mellin-Barnes Integrals. Cambridge University Press, Cambridge.
  • R. B. Paris (1992b) Smoothing of the Stokes phenomenon using Mellin-Barnes integrals. J. Comput. Appl. Math. 41 (1-2), pp. 117–133.
  • 8: 13.4 Integral Representations
    §13.4(iii) MellinBarnes Integrals
    9: 13.16 Integral Representations
    §13.16(iii) MellinBarnes Integrals
    10: 11.5 Integral Representations
    MellinBarnes Integrals