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Bailey–Daum q-Kummer sum

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1: 17.6 ϕ 1 2 Function
q -Gauss Sum
First q -Chu–Vandermonde Sum
Second q -Chu–Vandermonde Sum
Andrews–Askey Sum
BaileyDaum q -Kummer Sum
2: 17.12 Bailey Pairs
§17.12 Bailey Pairs
Bailey Transform
Bailey Pairs
Weak Bailey Lemma
Strong Bailey Lemma
3: 17 q-Hypergeometric and Related Functions
Chapter 17 q -Hypergeometric and Related Functions
4: 17.8 Special Cases of ψ r r Functions
17.8.1 n = - ( - z ) n q n ( n - 1 ) / 2 = ( q , z , q / z ; q ) ;
17.8.3 n = - ( - 1 ) n q n ( 3 n - 1 ) / 2 z 3 n ( 1 + z q n ) = ( q , - z , - q / z ; q ) ( q z 2 , q / z 2 ; q 2 ) .
Bailey’s Bilateral Summations
Sum Related to (17.6.4)
5: 4.48 Software
  • Bailey (1993). Fortran.

  • See also Bailey (1995), Hull and Abrham (1986), Xu and Li (1994). …
    6: 17.1 Special Notation
    f ( χ 1 ; χ 2 , , χ n ) + idem ( χ 1 ; χ 2 , , χ n ) = j = 1 n f ( χ j ; χ 1 , χ 2 , , χ j - 1 , χ j + 1 , , χ n ) .
    A slightly different notation is that in Bailey (1964) and Slater (1966); see §17.4(i). …
    7: 17.10 Transformations of ψ r r Functions
    §17.10 Transformations of ψ r r Functions
    Bailey’s ψ 2 2 Transformations
    17.10.4 ψ 2 2 ( e , f a q / c , a q / d ; q , a q e f ) = ( q / c , q / d , a q / e , a q / f ; q ) ( a q , q / a , a q / ( c d ) , a q / ( e f ) ; q ) n = - ( 1 - a q 2 n ) ( c , d , e , f ; q ) n ( 1 - a ) ( a q / c , a q / d , a q / e , a q / f ; q ) n ( q a 3 c d e f ) n q n 2 .
    8: 17.7 Special Cases of Higher ϕ s r Functions
    q -Analog of Bailey’s F 1 2 ( - 1 ) Sum
    Sum Related to (17.6.4)
    First q -Analog of Bailey’s F 3 4 ( 1 ) Sum
    Second q -Analog of Bailey’s F 3 4 ( 1 ) Sum
    Bailey’s Nonterminating Extension of Jackson’s ϕ 7 8 Sum
    9: 16.12 Products
    10: Bibliography B
  • D. H. Bailey (1993) Algorithm 719: Multiprecision translation and execution of Fortran programs. ACM Trans. Math. Software 19 (3), pp. 288–319.
  • D. H. Bailey (1995) A Fortran-90 based multiprecision system. ACM Trans. Math. Software 21 (4), pp. 379–387.
  • W. N. Bailey (1928) Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (2), pp. 242–254.
  • W. N. Bailey (1929) Transformations of generalized hypergeometric series. Proc. London Math. Soc. (2) 29 (2), pp. 495–502.
  • W. N. Bailey (1964) Generalized Hypergeometric Series. Stechert-Hafner, Inc., New York.