complex variables
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11—20 of 504 matching pages
11: 4.7 Derivatives and Differential Equations
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4.7.1
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- Symbols:
- : derivative of with respect to , : principal branch of logarithm function and : complex variable
- A&S Ref:
- 4.1.46
- Permalink:
- http://dlmf.nist.gov/4.7.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.7(i), §4.7 and Ch.4
4.7.6
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- Defines:
- : solution (locally)
- Symbols:
- : general logarithm function, : complex variable and : non-vanishing analytic function
- Permalink:
- http://dlmf.nist.gov/4.7.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.7(i), §4.7 and Ch.4
4.7.10
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- Symbols:
- : derivative of with respect to , : real or complex constant and : complex variable
- A&S Ref:
- 4.2.52
- Permalink:
- http://dlmf.nist.gov/4.7.E10
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.7(ii), §4.7 and Ch.4
4.7.14
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- Symbols:
- : derivative of with respect to , : real or complex constant and : complex variable
- Permalink:
- http://dlmf.nist.gov/4.7.E14
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.7(ii), §4.7 and Ch.4
4.7.15
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- Symbols:
- : base of natural logarithm, : real or complex constant, : complex variable, : arbitrary constant and : arbitrary constant
- Permalink:
- http://dlmf.nist.gov/4.7.E15
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.7(ii), §4.7 and Ch.4
12: 5.18 -Gamma and -Beta Functions
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5.18.1
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- Symbols:
- : -Pochhammer symbol (or -shifted factorial), : real or complex variable, : nonnegative integer, : nonnegative integer and : real or complex variable
- Permalink:
- http://dlmf.nist.gov/5.18.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.18(i), §5.18 and Ch.5
5.18.3
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- Symbols:
- : -Pochhammer symbol (or -shifted factorial), : real or complex variable, : nonnegative integer and : real or complex variable
- Permalink:
- http://dlmf.nist.gov/5.18.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.18(i), §5.18 and Ch.5
5.18.7
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- Symbols:
- : -gamma function, : real or complex variable and : complex variable
- Permalink:
- http://dlmf.nist.gov/5.18.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.18(ii), §5.18 and Ch.5
5.18.10
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- Symbols:
- : gamma function, : -gamma function, : real or complex variable and : complex variable
- Permalink:
- http://dlmf.nist.gov/5.18.E10
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.18(ii), §5.18 and Ch.5
5.18.11
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- Defines:
- : -beta function
- Symbols:
- : -gamma function, : real or complex variable, : real or complex variable and : real or complex variable
- Permalink:
- http://dlmf.nist.gov/5.18.E11
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.18(iii), §5.18 and Ch.5
13: 28.19 Expansions in Series of Functions
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28.19.1
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : base of natural logarithm, : imaginary unit, : complex variable, : complex parameter and : function
- Permalink:
- http://dlmf.nist.gov/28.19.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.19 and Ch.28
28.19.2
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- Defines:
- : function (locally)
- Symbols:
- : Mathieu function, : parameter, : integer, : complex variable, : complex parameter and : coefficients
- Referenced by:
- §28.19
- Permalink:
- http://dlmf.nist.gov/28.19.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.19 and Ch.28
28.19.3
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- Defines:
- : coefficients (locally)
- Symbols:
- : Mathieu function, : the ratio of the circumference of a circle to its diameter, : differential of , : integral, : parameter, : integer, : complex variable, : complex parameter and : function
- Permalink:
- http://dlmf.nist.gov/28.19.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.19 and Ch.28
28.19.4
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- Symbols:
- : Mathieu function, : base of natural logarithm, : imaginary unit, : parameter, : integer, : complex variable, : complex parameter and : coefficients
- Permalink:
- http://dlmf.nist.gov/28.19.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.19, §28.19 and Ch.28
14: 7.4 Symmetry
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7.4.1
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- Symbols:
- : error function and : complex variable
- A&S Ref:
- 7.1.9
- Permalink:
- http://dlmf.nist.gov/7.4.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.4 and Ch.7
7.4.2
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- Symbols:
- : complementary error function and : complex variable
- Permalink:
- http://dlmf.nist.gov/7.4.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.4 and Ch.7
7.4.3
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- Symbols:
- : Faddeeva (or Faddeyeva) function, : base of natural logarithm and : complex variable
- A&S Ref:
- 7.1.11
- Permalink:
- http://dlmf.nist.gov/7.4.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.4 and Ch.7
7.4.4
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- Symbols:
- : Dawson’s integral and : complex variable
- Permalink:
- http://dlmf.nist.gov/7.4.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.4 and Ch.7
15: 4.22 Infinite Products and Partial Fractions
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4.22.1
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : sine function, : integer and : complex variable
- A&S Ref:
- 4.3.89
- Permalink:
- http://dlmf.nist.gov/4.22.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.22 and Ch.4
4.22.2
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : cosine function, : integer and : complex variable
- A&S Ref:
- 4.3.90
- Permalink:
- http://dlmf.nist.gov/4.22.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.22 and Ch.4
4.22.3
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : cotangent function, : integer and : complex variable
- A&S Ref:
- 4.3.91
- Referenced by:
- §22.12
- Permalink:
- http://dlmf.nist.gov/4.22.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.22 and Ch.4
4.22.4
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : cosecant function, : integer and : complex variable
- A&S Ref:
- 4.3.92
- Permalink:
- http://dlmf.nist.gov/4.22.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.22 and Ch.4
4.22.5
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : cosecant function, : integer and : complex variable
- A&S Ref:
- 4.3.93
- Referenced by:
- §22.12
- Permalink:
- http://dlmf.nist.gov/4.22.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.22 and Ch.4
16: 4.36 Infinite Products and Partial Fractions
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4.36.1
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : hyperbolic sine function, : integer and : complex variable
- A&S Ref:
- 4.5.68
- Permalink:
- http://dlmf.nist.gov/4.36.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.36 and Ch.4
4.36.2
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : hyperbolic cosine function, : integer and : complex variable
- A&S Ref:
- 4.5.69
- Permalink:
- http://dlmf.nist.gov/4.36.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.36 and Ch.4
4.36.3
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : hyperbolic cotangent function, : integer and : complex variable
- Permalink:
- http://dlmf.nist.gov/4.36.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.36 and Ch.4
4.36.4
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : hyperbolic cosecant function, : imaginary unit, : integer and : complex variable
- Permalink:
- http://dlmf.nist.gov/4.36.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.36 and Ch.4
4.36.5
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : hyperbolic cosecant function, : integer and : complex variable
- Permalink:
- http://dlmf.nist.gov/4.36.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.36 and Ch.4
17: 10.13 Other Differential Equations
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10.13.1
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- Symbols:
- : cylinder function, : complex variable and : complex parameter
- A&S Ref:
- 9.1.49
- Referenced by:
- §1.18(vi), §10.36
- Permalink:
- http://dlmf.nist.gov/10.13.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.13 and Ch.10
10.13.2
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- Symbols:
- : cylinder function, : complex variable and : complex parameter
- A&S Ref:
- 9.1.50
- Permalink:
- http://dlmf.nist.gov/10.13.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.13 and Ch.10
10.13.5
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- Symbols:
- : cylinder function, : complex variable and : complex parameter
- A&S Ref:
- 9.1.53
- Permalink:
- http://dlmf.nist.gov/10.13.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.13 and Ch.10
10.13.9
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- Symbols:
- : cylinder function, : complex variable, : complex parameter and : cylinder function
- A&S Ref:
- 9.1.58 (modified)
- Referenced by:
- §10.13, §10.36
- Permalink:
- http://dlmf.nist.gov/10.13.E9
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.13 and Ch.10
10.13.10
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- Symbols:
- : cylinder function, : complex variable, : complex parameter and : cylinder function
- A&S Ref:
- 9.1.59
- Permalink:
- http://dlmf.nist.gov/10.13.E10
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.13 and Ch.10
18: 12.8 Recurrence Relations and Derivatives
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12.8.1
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- Symbols:
- : parabolic cylinder function, : complex variable and : real or complex parameter
- A&S Ref:
- 19.6.4
- Referenced by:
- §12.8(i)
- Permalink:
- http://dlmf.nist.gov/12.8.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §12.8(i), §12.8 and Ch.12
12.8.2
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- Symbols:
- : parabolic cylinder function, : complex variable and : real or complex parameter
- A&S Ref:
- 19.6.1
- Permalink:
- http://dlmf.nist.gov/12.8.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §12.8(i), §12.8 and Ch.12
12.8.3
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- Symbols:
- : parabolic cylinder function, : complex variable and : real or complex parameter
- A&S Ref:
- 19.6.2
- Permalink:
- http://dlmf.nist.gov/12.8.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §12.8(i), §12.8 and Ch.12
12.8.4
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- Symbols:
- : parabolic cylinder function, : complex variable and : real or complex parameter
- A&S Ref:
- 19.6.3
- Referenced by:
- §12.8(i)
- Permalink:
- http://dlmf.nist.gov/12.8.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §12.8(i), §12.8 and Ch.12
12.8.5
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- Symbols:
- : parabolic cylinder function, : complex variable and : real or complex parameter
- A&S Ref:
- 19.6.8
- Permalink:
- http://dlmf.nist.gov/12.8.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §12.8(i), §12.8 and Ch.12
19: 5.12 Beta Function
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5.12.1
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- Defines:
- : beta function
- Symbols:
- : gamma function, : differential of , : integral, : real or complex variable and : real or complex variable
- A&S Ref:
- 6.2.1 and 6.2.2
- Referenced by:
- §10.22(ii), §10.43(iii), §19.20(i), §19.20(iv), §2.6(iii), §5.12, §5.12, §7.7(ii)
- Permalink:
- http://dlmf.nist.gov/5.12.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.12, §5.12 and Ch.5
5.12.3
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- Symbols:
- : beta function, : differential of , : integral, : real or complex variable and : real or complex variable
- A&S Ref:
- 6.2.1 and 6.2.2
- Referenced by:
- §5.12
- Permalink:
- http://dlmf.nist.gov/5.12.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.12, §5.12 and Ch.5
5.12.4
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- Symbols:
- : beta function, : the ratio of the circumference of a circle to its diameter, : differential of , : integral, : phase, : complex variable, : real or complex variable and : real or complex variable
- Referenced by:
- §5.12, §5.12
- Permalink:
- http://dlmf.nist.gov/5.12.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.12, §5.12 and Ch.5
5.12.8
, , .
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- Symbols:
- : beta function, : the ratio of the circumference of a circle to its diameter, : differential of , : imaginary unit, : integral, : real part, : real or complex variable, : complex variable, : real or complex variable and : real or complex variable
- Referenced by:
- §5.12, §5.12
- Permalink:
- http://dlmf.nist.gov/5.12.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.12, §5.12 and Ch.5
5.12.12
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- Symbols:
- : beta function, : the ratio of the circumference of a circle to its diameter, : differential of , : base of natural logarithm, : imaginary unit, : integral, : sine function, : real or complex variable, : real or complex variable and : point
- Referenced by:
- §5.12, §5.12
- Permalink:
- http://dlmf.nist.gov/5.12.E12
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.12, §5.12 and Ch.5
20: 4.21 Identities
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4.21.12
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- Symbols:
- : cosine function, : sine function and : complex variable
- A&S Ref:
- 4.3.10
- Permalink:
- http://dlmf.nist.gov/4.21.E12
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.21(ii), §4.21 and Ch.4
4.21.13
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- Symbols:
- : secant function, : tangent function and : complex variable
- A&S Ref:
- 4.3.11
- Permalink:
- http://dlmf.nist.gov/4.21.E13
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.21(ii), §4.21 and Ch.4
4.21.14
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- Symbols:
- : cosecant function, : cotangent function and : complex variable
- A&S Ref:
- 4.3.12
- Permalink:
- http://dlmf.nist.gov/4.21.E14
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.21(ii), §4.21 and Ch.4
4.21.24
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- Symbols:
- : sine function and : complex variable
- A&S Ref:
- 4.3.13
- Permalink:
- http://dlmf.nist.gov/4.21.E24
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.21(iii), §4.21 and Ch.4
4.21.25
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- Symbols:
- : cosine function and : complex variable
- A&S Ref:
- 4.3.14
- Permalink:
- http://dlmf.nist.gov/4.21.E25
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.21(iii), §4.21 and Ch.4