q-hypergeometric%20function
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11: 16.13 Appell Functions
§16.13 Appell Functions
►The following four functions of two real or complex variables and cannot be expressed as a product of two functions, in general, but they satisfy partial differential equations that resemble the hypergeometric differential equation (15.10.1): ►
16.13.1
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16.13.4
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12: 15.2 Definitions and Analytical Properties
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§15.2(i) Gauss Series
►The hypergeometric function is defined by the Gauss series … … ►On the circle of convergence, , the Gauss series: … ►§15.2(ii) Analytic Properties
…13: 5.12 Beta Function
14: 14.20 Conical (or Mehler) Functions
§14.20 Conical (or Mehler) Functions
►§14.20(i) Definitions and Wronskians
… ► … ►§14.20(ii) Graphics
… ►§14.20(x) Zeros and Integrals
…15: 17.17 Physical Applications
§17.17 Physical Applications
… ►They were given this name because they play a role in quantum physics analogous to the role of Lie groups and special functions in classical mechanics. See Kassel (1995). …16: 17.15 Generalizations
§17.15 Generalizations
►For higher-dimensional basic hypergometric functions, see Milne (1985a, b, c, d, 1988, 1994, 1997) and Gustafson (1987).17: 10.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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►For the spherical Bessel functions and modified spherical Bessel functions the order is a nonnegative integer.
For the other functions when the order is replaced by , it can be any integer.
For the Kelvin functions the order is always assumed to be real.
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►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).