q-Pfaff--Saalschutz sum
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1: 16.4 Argument Unity
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►When the function is said to be balanced or Saalschützian.
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Lerch Sum
… ►Pfaff–Saalschütz Balanced Sum
… ►Džrbasjan’s Sum
…2: 17.4 Basic Hypergeometric Functions
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►In these references the factor is not included in the sum.
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17.4.3
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17.4.5
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17.4.7
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►The series (17.4.1) is said to be balanced or Saalschützian when it terminates, , , and
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3: 35.8 Generalized Hypergeometric Functions of Matrix Argument
4: 17.7 Special Cases of Higher Functions
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Sum Related to (17.6.4)
… ►-Pfaff–Saalschütz Sum
… ►Nonterminating Form of the -Saalschütz Sum
… ►Gasper–Rahman -Analogs of the Karlsson–Minton Sums
… ►Gosper’s Bibasic Sum
…5: 4.27 Sums
§4.27 Sums
►For sums of trigonometric and inverse trigonometric functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §§14–42), Oberhettinger (1973), and Prudnikov et al. (1986a, Chapter 5).6: 24.1 Special Notation
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►It was used in Saalschütz (1893), Nielsen (1923), Schwatt (1962), and Whittaker and Watson (1927).
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7: 4.11 Sums
§4.11 Sums
…8: 4.41 Sums
§4.41 Sums
►For sums of hyperbolic functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §43), Prudnikov et al. (1986a, §5.3), and Zucker (1979).9: 7.15 Sums
§7.15 Sums
►For sums involving the error function see Hansen (1975, p. 423) and Prudnikov et al. (1986b, vol. 2, pp. 650–651).10: Bibliography K
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The computation of the sums of negative even powers of roots of Bessel functions.
Doklady Akad. Nauk SSSR (N.S.) 77, pp. 561–564.
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An extension of Saalschütz’s summation theorem for the series
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Integral Transforms Spec. Funct. 24 (11), pp. 916–921.
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Estimates of trigonometric sums and their applications.
Uspehi Mat. Nauk 13 (4 (82)), pp. 185–192 (Russian).
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HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
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