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21: 16.4 Argument Unity
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βΊ
16.4.2_5
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βΊ
β
- Symbols:
-
or : alternatively
or
generalized hypergeometric function, : Pochhammer’s symbol (or shifted factorial) and : real or complex parameters - Source:
- Lerch (1905, (3))
- Referenced by:
- §16.4(ii)
- Permalink:
- http://dlmf.nist.gov/16.4.E2_5
- Encodings:
- pMML, png, TeX
- Addition (effective with 1.1.0):
- This equation was added.
- See also:
- Annotations for §16.4(ii), §16.4(ii), §16.4 and Ch.16
16.4.3
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βΊ
β
- Symbols:
-
or : alternatively
or
generalized hypergeometric function, : Pochhammer’s symbol (or shifted factorial), : real or complex parameters and : real or complex parameters - Referenced by:
- §18.17(vii)
- Permalink:
- http://dlmf.nist.gov/16.4.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.4(ii), §16.4(ii), §16.4 and Ch.16
16.4.5
…
βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : factorial (as in ) and : real or complex parameters - Permalink:
- http://dlmf.nist.gov/16.4.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.4(ii), §16.4(ii), §16.4 and Ch.16
16.4.7
…
βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : the ratio of the circumference of a circle to its diameter and : real or complex parameters - Referenced by:
- §16.4(ii), §17.7(iii), Erratum (V1.1.11) for Subsection 17.7(iii)
- Permalink:
- http://dlmf.nist.gov/16.4.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.4(ii), §16.4(ii), §16.4 and Ch.16
16.4.8
.
…
β
- Symbols:
-
or : alternatively
or
generalized hypergeometric function, : Pochhammer’s symbol (or shifted factorial) and : real or complex parameters - Permalink:
- http://dlmf.nist.gov/16.4.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.4(ii), §16.4(ii), §16.4 and Ch.16
22: 16.8 Differential Equations
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βΊ
16.8.7
,
…
βΊ
β
- Symbols:
-
or : alternatively
or
generalized hypergeometric function, : nonnegative integer, : complex variable, : real or complex parameters, : real or complex parameters and : solution - Permalink:
- http://dlmf.nist.gov/16.8.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.8(ii), §16.8 and Ch.16
16.8.8
.
…
βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : the ratio of the circumference of a circle to its diameter, : phase, : nonnegative integer, : complex variable, : real or complex parameters, : real or complex parameters and : solution - Referenced by:
- §16.11(ii)
- Permalink:
- http://dlmf.nist.gov/16.8.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.8(ii), §16.8 and Ch.16
16.8.9
…
βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : factorial (as in ), : nonnegative integer, : complex variable, : real or complex parameters and : real or complex parameters - Referenced by:
- §16.8(ii)
- Permalink:
- http://dlmf.nist.gov/16.8.E9
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.8(ii), §16.8 and Ch.16
16.8.10
…
βΊ
β
- Symbols:
-
or : alternatively
or
generalized hypergeometric function, : nonnegative integer, : nonnegative integer, : complex variable, : real or complex parameters and : real or complex parameters - Permalink:
- http://dlmf.nist.gov/16.8.E10
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.8(iii), §16.8 and Ch.16
16.8.11
…
β
- Symbols:
-
or : alternatively
or
generalized hypergeometric function, : nonnegative integer, : nonnegative integer, : complex variable, : real or complex parameters and : real or complex parameters - Permalink:
- http://dlmf.nist.gov/16.8.E11
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.8(iii), §16.8 and Ch.16
23: 16.11 Asymptotic Expansions
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βΊ
16.11.6
;
…
βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : the ratio of the circumference of a circle to its diameter, : phase, : nonnegative integer, : complex variable, : real or complex parameters, : real or complex parameters and : formal infinite series - Permalink:
- http://dlmf.nist.gov/16.11.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.11(ii), §16.11(ii), §16.11 and Ch.16
16.11.7
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βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : Poincaré asymptotic expansion, : the ratio of the circumference of a circle to its diameter, : base of natural logarithm, : imaginary unit, : nonnegative integer, : complex variable, : real or complex parameters, : real or complex parameters, : formal infinite series and : formal infinite series - Referenced by:
- §16.11(ii)
- Permalink:
- http://dlmf.nist.gov/16.11.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.11(ii), §16.11(ii), §16.11 and Ch.16
16.11.8
…
βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : Poincaré asymptotic expansion, : the ratio of the circumference of a circle to its diameter, : imaginary unit, : nonnegative integer, : complex variable, : real or complex parameters, : real or complex parameters, : formal infinite series, : formal infinite series and - Permalink:
- http://dlmf.nist.gov/16.11.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.11(ii), §16.11(ii), §16.11 and Ch.16
16.11.9
…
βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : Poincaré asymptotic expansion, : the ratio of the circumference of a circle to its diameter, : imaginary unit, : nonnegative integer, : nonnegative integer, : complex variable, : real or complex parameters, : real or complex parameters, : formal infinite series and - Referenced by:
- §16.11(ii)
- Permalink:
- http://dlmf.nist.gov/16.11.E9
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.11(ii), §16.11(ii), §16.11 and Ch.16
16.11.11
…
β
- Symbols:
-
: order not exceeding,
or : alternatively
or
generalized hypergeometric function, : Pochhammer’s symbol (or shifted factorial), : factorial (as in ), : nonnegative integer, : nonnegative integer, : complex variable, : real or complex parameters, : real or complex parameters and : large parameter - Permalink:
- http://dlmf.nist.gov/16.11.E11
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.11(iii), §16.11 and Ch.16
24: 10.1 Special Notation
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βΊA common alternative notation for is .
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25: 8.1 Special Notation
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βΊAlternative notations include: Prym’s functions
, , Nielsen (1906a, pp. 25–26), Batchelder (1967, p. 63); , , Dingle (1973); , , Magnus et al. (1966); , , Luke (1975).
26: 16.1 Special Notation
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βΊAlternative notations are , , and for the generalized hypergeometric function, , , , , for the Appell functions, and for the Meijer -function.
27: 16.5 Integral Representations and Integrals
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βΊ
16.5.1
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βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : the ratio of the circumference of a circle to its diameter, : differential of , : imaginary unit, : integral, : nonnegative integer, : nonnegative integer, : complex variable, : real or complex parameters and : real or complex parameters - Referenced by:
- §13.6(vi), §16.11(i), §16.5, §16.5
- Permalink:
- http://dlmf.nist.gov/16.5.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.5 and Ch.16
16.5.2
,
βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : differential of , : integral, : real part, : nonnegative integer, : nonnegative integer, : complex variable, : real or complex parameters and : real or complex parameters - Keywords:
- Mellin transform
- Referenced by:
- §16.5, §16.5
- Permalink:
- http://dlmf.nist.gov/16.5.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.5 and Ch.16
16.5.3
, ,
βΊ
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : differential of , : base of natural logarithm, : integral, : real part, : nonnegative integer, : nonnegative integer, : complex variable, : real or complex parameters and : real or complex parameters - Keywords:
- Laplace transform, Mellin transform
- Referenced by:
- §16.5
- Permalink:
- http://dlmf.nist.gov/16.5.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.5 and Ch.16
16.5.4
, .
…
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, : the ratio of the circumference of a circle to its diameter, : differential of , : base of natural logarithm, : imaginary unit, : integral, : real part, : nonnegative integer, : nonnegative integer, : complex variable, : real or complex parameters and : real or complex parameters - Keywords:
- Mellin transform
- Referenced by:
- §16.5, §16.5
- Permalink:
- http://dlmf.nist.gov/16.5.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.5 and Ch.16
28: 16.18 Special Cases
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βΊ
16.18.1
…
β
- Symbols:
-
: gamma function,
or : alternatively
or
generalized hypergeometric function, or : Meijer -function, : nonnegative integer, : nonnegative integer, : complex variable, : real or complex parameters and : real or complex parameters - Permalink:
- http://dlmf.nist.gov/16.18.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.18 and Ch.16
29: 16.23 Mathematical Applications
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βΊ
16.23.1
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β
- Symbols:
-
or : alternatively
or
generalized hypergeometric function - Permalink:
- http://dlmf.nist.gov/16.23.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §16.23(iii), §16.23 and Ch.16