메뉴 건너뛰기




Volumn 162, Issue 2, 2005, Pages 931-947

A unified presentation of the Gamma-type functions occurring in diffraction theory and associated probability distributions

Author keywords

Diffraction theory; Gamma and incomplete Gamma functions; Generalized hypergeometric function; Hazard (or failure) rate function; Moment generating function; Probability density function; Survival (or reliability) function; Wiener hopf technique

Indexed keywords

ASYMPTOTIC STABILITY; DIFFRACTION; MATHEMATICAL TRANSFORMATIONS; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS;

EID: 10444258027     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.12.133     Document Type: Article
Times cited : (30)

References (33)
  • 1
    • 0042793291 scopus 로고    scopus 로고
    • A generalized inverse Gaussian distribution with τ-confluent hypergeometric function
    • I. Ali, S.L. Kalla, H.G. Khajah, A generalized inverse Gaussian distribution with τ-confluent hypergeometric function, Integral Transform. Spec. Funct. 12 (2001) 101-114.
    • (2001) Integral Transform. Spec. Funct. , vol.12 , pp. 101-114
    • Ali, I.1    Kalla, S.L.2    Khajah, H.G.3
  • 2
    • 85012279088 scopus 로고    scopus 로고
    • Asymptotic expansions for the generalized Gamma and incomplete Gamma functions
    • F. Al-Musallam, S.L. Kalla, Asymptotic expansions for the generalized Gamma and incomplete Gamma functions, Appl. Anal. 66 (1997) 173-187.
    • (1997) Appl. Anal. , vol.66 , pp. 173-187
    • Al-Musallam, F.1    Kalla, S.L.2
  • 3
    • 0011124830 scopus 로고    scopus 로고
    • Further results on a generalized Gamma function occurring in diffraction theory
    • F. Al-Musallam, S.L. Kalla, Further results on a generalized Gamma function occurring in diffraction theory, Integral Transform. Spec. Funct. 7 (1998) 175-190.
    • (1998) Integral Transform. Spec. Funct. , vol.7 , pp. 175-190
    • Al-Musallam, F.1    Kalla, S.L.2
  • 4
    • 10444286153 scopus 로고    scopus 로고
    • On a probability distribution involving a τ-confluent hypergeometric function of two variables
    • B.N. Al-Saqabi, S.L. Kalla, A. Shafea, On a probability distribution involving a τ-confluent hypergeometric function of two variables, Algebras Groups Geom. 19 (2002) 254-275.
    • (2002) Algebras Groups Geom. , vol.19 , pp. 254-275
    • Al-Saqabi, B.N.1    Kalla, S.L.2    Shafea, A.3
  • 5
    • 10444228376 scopus 로고    scopus 로고
    • An extension of some hypergeometric functions of two variables
    • A.H. Al-Shammery, S.L. Kalla, An extension of some hypergeometric functions of two variables, Rev. Acad. Canaria Cienc. 12 (2000) 189-196.
    • (2000) Rev. Acad. Canaria Cienc. , vol.12 , pp. 189-196
    • Al-Shammery, A.H.1    Kalla, S.L.2
  • 6
    • 0347084839 scopus 로고    scopus 로고
    • On a generalized Gamma-type distribution with τ-confluent hypergeometric function
    • A. Al-Zamel, On a generalized Gamma-type distribution with τ-confluent hypergeometric function, Kuwait J. Sci. Tech. 28 (2001) 25-36.
    • (2001) Kuwait J. Sci. Tech. , vol.28 , pp. 25-36
    • Al-Zamel, A.1
  • 7
    • 10444271215 scopus 로고    scopus 로고
    • A unified form of Gamma-type and inverse Gaussian distributions
    • A. Al-Zamel, I. Ali, S.L. Kalla, A unified form of Gamma-type and inverse Gaussian distributions, Hadronic J. 25 (2002) 1-21.
    • (2002) Hadronic J. , vol.25 , pp. 1-21
    • Al-Zamel, A.1    Ali, I.2    Kalla, S.L.3
  • 8
    • 10444256719 scopus 로고    scopus 로고
    • A generalized Beta function and associated probability density
    • Y. Ben Nakhi, S.L. Kalla, A generalized Beta function and associated probability density, Internat. J. Math. Math. Sci. 8 (2002) 467-478.
    • (2002) Internat. J. Math. Math. Sci. , vol.8 , pp. 467-478
    • Nakhi, Y.B.1    Kalla, S.L.2
  • 9
    • 10444231444 scopus 로고    scopus 로고
    • A generalization of Beta-type distribution with ω-appell function
    • Y. Ben Nakhi, S.L. Kalla, A generalization of Beta-type distribution with ω-Appell function, Integral Transform. Spec. Funct. 14 (2003) 321-332.
    • (2003) Integral Transform. Spec. Funct. , vol.14 , pp. 321-332
    • Nakhi, Y.B.1    Kalla, S.L.2
  • 11
    • 0007268717 scopus 로고
    • The asymptotic expansion of generalized hypergeometric functions
    • C. Fox, The asymptotic expansion of generalized hypergeometric functions, Proc. London Math. Soc. (Ser. 2) 27 (1928) 389-400.
    • (1928) Proc. London Math. Soc. (Ser. 2) , vol.27 , pp. 389-400
    • Fox, C.1
  • 12
    • 0037465592 scopus 로고    scopus 로고
    • Further results on generalized hypergeometric functions
    • L. Galué, A. Al-Zamel, S.L. Kalla, Further results on generalized hypergeometric functions, Appl. Math. Comput. 136 (2003) 17-25.
    • (2003) Appl. Math. Comput. , vol.136 , pp. 17-25
    • Galué, L.1    Al-Zamel, A.2    Kalla, S.L.3
  • 13
    • 0038643419 scopus 로고    scopus 로고
    • On a recent generalization of Gamma distribution
    • M.E. Ghitany, On a recent generalization of Gamma distribution, Comm. Statist. Theory Methods 27 (1998) 223-233.
    • (1998) Comm. Statist. Theory Methods , vol.27 , pp. 223-233
    • Ghitany, M.E.1
  • 16
    • 0010933261 scopus 로고
    • Statistical properties of the generalized inverse Gaussian distribution
    • Springer-Verlag, New York and Berlin
    • B. Jorgensen, Statistical Properties of the Generalized Inverse Gaussian Distribution, in: Lecture Notes in Statistics, vol. 9, Springer-Verlag, New York and Berlin, 1982.
    • (1982) Lecture Notes in Statistics , vol.9
    • Jorgensen, B.1
  • 17
    • 10444247607 scopus 로고    scopus 로고
    • Further results on a unified form of Gamma-type distribution
    • S.L. Kalla, B.N. Al-Saqabi, Further results on a unified form of Gamma-type distribution, Fract. Calc. Appl. Anal. 4 (2001) 91-100.
    • (2001) Fract. Calc. Appl. Anal. , vol.4 , pp. 91-100
    • Kalla, S.L.1    Al-Saqabi, B.N.2
  • 19
    • 0003180827 scopus 로고
    • On generalized Gamma functions occurring in diffraction theory
    • K. Kobayashi, On generalized Gamma functions occurring in diffraction theory, J. Phys. Soc. Japan 60 (1991) 1501-1512.
    • (1991) J. Phys. Soc. Japan , vol.60 , pp. 1501-1512
    • Kobayashi, K.1
  • 20
    • 0011092354 scopus 로고
    • Plane wave diffraction by a strip: Exact and asymptotic solutions
    • K. Kobayashi, Plane wave diffraction by a strip: Exact and asymptotic solutions, J. Phys. Soc. Japan 60 (1991) 1891-1905.
    • (1991) J. Phys. Soc. Japan , vol.60 , pp. 1891-1905
    • Kobayashi, K.1
  • 21
    • 10444274455 scopus 로고    scopus 로고
    • A probability density function involving a generalized hypergeometric function
    • J. Matera, Y. Ben Nakhi, S.L. Kalla, A probability density function involving a generalized hypergeometric function, Internat. J. Appl. Math. 7 (2001) 389-403.
    • (2001) Internat. J. Appl. Math. , vol.7 , pp. 389-403
    • Matera, J.1    Nakhi, Y.B.2    Kalla, S.L.3
  • 23
    • 0003260997 scopus 로고
    • Generalized hypergeometric functions with applications in statistics and physical sciences
    • Springer-Verlag, Berlin, Heidelberg and New York
    • A.M. Mathai, R.K. Saxena, Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, in: Lecture Notes in Mathematics, vol. 348, Springer-Verlag, Berlin, Heidelberg and New York, 1973.
    • (1973) Lecture Notes in Mathematics , vol.348
    • Mathai, A.M.1    Saxena, R.K.2
  • 25
    • 10444259218 scopus 로고    scopus 로고
    • On a generalized Gamma function occurring in diffraction theory
    • R.K. Saxena, S.L. Kalla, On a generalized Gamma function occurring in diffraction theory, Internat. J. Appl. Math. 5 (2001) 189-202.
    • (2001) Internat. J. Appl. Math. , vol.5 , pp. 189-202
    • Saxena, R.K.1    Kalla, S.L.2
  • 26
    • 10444237516 scopus 로고
    • On Eulerian integrals associated with Kampé de Fériet's function
    • H.M. Srivastava, M.C. Daoust, On Eulerian integrals associated with Kampé de Fériet's function, Publ. Inst. Math. (Beograd) (New Ser.) 9 (23) (1969) 199-202.
    • (1969) Publ. Inst. Math. (Beograd) (New Ser.) , vol.9 , Issue.23 , pp. 199-202
    • Srivastava, H.M.1    Daoust, M.C.2
  • 27
    • 0000825213 scopus 로고
    • Certain generalized Neumann expansions associated with the Kampé de Fériet function
    • H.M. Srivastava, M.C. Daoust, Certain generalized Neumann expansions associated with the Kampé de Fériet function, Nederl. Akad. Wetensch. Indag. Math. 31 (1969) 449-457.
    • (1969) Nederl. Akad. Wetensch. Indag. Math. , vol.31 , pp. 449-457
    • Srivastava, H.M.1    Daoust, M.C.2
  • 29
    • 0003791753 scopus 로고
    • Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto
    • H.M. Srivastava, P.W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.
    • (1985) Multiple Gaussian Hypergeometric Series
    • Srivastava, H.M.1    Karlsson, P.W.2
  • 30
    • 0011141549 scopus 로고    scopus 로고
    • On some generalizations of the functions of hypergeometric type
    • N. Virchenko, On some generalizations of the functions of hypergeometric type, Fract. Calc. Appl. Anal. 2 (1999) 233-244.
    • (1999) Fract. Calc. Appl. Anal. , vol.2 , pp. 233-244
    • Virchenko, N.1
  • 32
    • 84963044459 scopus 로고
    • The asymptotic expansion of the generalized hypergeometric function
    • E.M. Wright, The asymptotic expansion of the generalized hypergeometric function, J. London Math. Soc. 10 (1935) 286-293.
    • (1935) J. London Math. Soc. , vol.10 , pp. 286-293
    • Wright, E.M.1
  • 33
    • 84963078619 scopus 로고
    • The asymptotic expansion of the generalized hypergeometric function
    • E.M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc. London Math. Soc. (Ser. 2) 46 (1940) 389-408.
    • (1940) Proc. London Math. Soc. (Ser. 2) , vol.46 , pp. 389-408
    • Wright, E.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.