complex variables
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21—30 of 504 matching pages
21: 4.33 Maclaurin Series and Laurent Series
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4.33.1
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- Symbols:
- : factorial (as in ), : hyperbolic sine function and : complex variable
- A&S Ref:
- 4.5.62
- Permalink:
- http://dlmf.nist.gov/4.33.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.33 and Ch.4
4.33.2
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- Symbols:
- : factorial (as in ), : hyperbolic cosine function and : complex variable
- A&S Ref:
- 4.5.63
- Permalink:
- http://dlmf.nist.gov/4.33.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.33 and Ch.4
4.33.3
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- Symbols:
- : Bernoulli numbers, : the ratio of the circumference of a circle to its diameter, : factorial (as in ), : hyperbolic tangent function, : integer and : complex variable
- A&S Ref:
- 4.5.64
- Permalink:
- http://dlmf.nist.gov/4.33.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.33 and Ch.4
22: 33.13 Complex Variable and Parameters
§33.13 Complex Variable and Parameters
…23: 5.13 Integrals
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5.13.1
, ,
.
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- Symbols:
- : gamma function, : the ratio of the circumference of a circle to its diameter, : differential of , : imaginary unit, : integral, : phase, : real part, : real or complex variable, : complex variable, : real or complex variable and : real or complex variable
- Referenced by:
- §5.13, §5.13, §5.19(ii)
- Permalink:
- http://dlmf.nist.gov/5.13.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.13 and Ch.5
5.13.2
, .
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- Symbols:
- : gamma 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 and : real or complex variable
- Referenced by:
- §5.13
- Permalink:
- http://dlmf.nist.gov/5.13.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.13 and Ch.5
5.13.3
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- Symbols:
- : gamma function, : the ratio of the circumference of a circle to its diameter, : differential of , : imaginary unit, : integral, : real part, : real or complex variable and : real or complex variable
- Referenced by:
- §5.13
- Permalink:
- http://dlmf.nist.gov/5.13.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.13, §5.13 and Ch.5
5.13.4
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- Symbols:
- : gamma function, : differential of , : integral, : real part, : real or complex variable and : real or complex variable
- Referenced by:
- §5.13
- Permalink:
- http://dlmf.nist.gov/5.13.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.13, §5.13 and Ch.5
5.13.5
, .
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- Symbols:
- : gamma function, : the ratio of the circumference of a circle to its diameter, : differential of , : imaginary unit, : integral, : real part, : nonnegative integer, : nonnegative integer and : real or complex variable
- Referenced by:
- §5.13
- Permalink:
- http://dlmf.nist.gov/5.13.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.13, §5.13 and Ch.5
24: 12.4 Power-Series Expansions
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12.4.1
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- Symbols:
- : parabolic cylinder function, : complex variable, : real or complex parameter, : solution and : solution
- Referenced by:
- §12.20
- Permalink:
- http://dlmf.nist.gov/12.4.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §12.4 and Ch.12
12.4.2
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- Symbols:
- : parabolic cylinder function, : complex variable, : real or complex parameter, : solution and : solution
- Referenced by:
- §12.20
- Permalink:
- http://dlmf.nist.gov/12.4.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §12.4 and Ch.12
12.4.3
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- Defines:
- : solution (locally)
- Symbols:
- : base of natural logarithm, : factorial (as in ), : complex variable and : real or complex parameter
- A&S Ref:
- 19.2.1 (modification of)
- Referenced by:
- §12.14(v), §12.7(iv)
- Permalink:
- http://dlmf.nist.gov/12.4.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §12.4 and Ch.12
12.4.5
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- Symbols:
- : base of natural logarithm, : factorial (as in ), : complex variable, : real or complex parameter and : solution
- A&S Ref:
- 19.2.2 (modification of)
- Permalink:
- http://dlmf.nist.gov/12.4.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §12.4 and Ch.12
12.4.6
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- Symbols:
- : base of natural logarithm, : factorial (as in ), : complex variable, : real or complex parameter and : solution
- A&S Ref:
- 19.2.4 (modification of)
- Referenced by:
- §12.14(v), §12.7(iv)
- Permalink:
- http://dlmf.nist.gov/12.4.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §12.4 and Ch.12
25: 4.8 Identities
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4.8.1
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- Symbols:
- : general logarithm function and : complex variable
- A&S Ref:
- 4.1.6
- Referenced by:
- §4.8(i)
- Permalink:
- http://dlmf.nist.gov/4.8.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.8(i), §4.8 and Ch.4
4.8.3
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- Symbols:
- : general logarithm function and : complex variable
- A&S Ref:
- 4.1.8
- Permalink:
- http://dlmf.nist.gov/4.8.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.8(i), §4.8 and Ch.4
4.8.5
,
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- Symbols:
- : element of, : set of all integers, : general logarithm function, : integer and : complex variable
- A&S Ref:
- 4.1.10
- Referenced by:
- §4.8(i)
- Permalink:
- http://dlmf.nist.gov/4.8.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.8(i), §4.8 and Ch.4
4.8.10
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- Symbols:
- : exponential function, : general logarithm function, : principal branch of logarithm function and : complex variable
- A&S Ref:
- 4.2.4
- Referenced by:
- (25.10.2), §4.8(i)
- Permalink:
- http://dlmf.nist.gov/4.8.E10
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.8(i), §4.8 and Ch.4
4.8.14
,
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- Symbols:
- : real or complex constant and : complex variable
- A&S Ref:
- 4.2.15
- Referenced by:
- Erratum (V1.0.20) for Equation (4.8.14)
- Permalink:
- http://dlmf.nist.gov/4.8.E14
- Encodings:
- pMML, png, TeX
- Clarification (effective with 1.0.20):
-
The constraint was added.
Suggested 2018-08-13 by Ted Ersek
- See also:
- Annotations for §4.8(ii), §4.8 and Ch.4
26: 4.35 Identities
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4.35.11
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- Symbols:
- : hyperbolic cosine function, : hyperbolic sine function and : complex variable
- A&S Ref:
- 4.5.16
- Permalink:
- http://dlmf.nist.gov/4.35.E11
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.35(ii), §4.35 and Ch.4
4.35.12
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- Symbols:
- : hyperbolic secant function, : hyperbolic tangent function and : complex variable
- A&S Ref:
- 4.5.17
- Permalink:
- http://dlmf.nist.gov/4.35.E12
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.35(ii), §4.35 and Ch.4
4.35.13
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- Symbols:
- : hyperbolic cosecant function, : hyperbolic cotangent function and : complex variable
- A&S Ref:
- 4.5.18
- Permalink:
- http://dlmf.nist.gov/4.35.E13
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.35(ii), §4.35 and Ch.4
4.35.23
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- Symbols:
- : hyperbolic sine function and : complex variable
- A&S Ref:
- 4.5.21
- Permalink:
- http://dlmf.nist.gov/4.35.E23
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.35(iii), §4.35 and Ch.4
4.35.24
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- Symbols:
- : hyperbolic cosine function and : complex variable
- A&S Ref:
- 4.5.22
- Permalink:
- http://dlmf.nist.gov/4.35.E24
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.35(iii), §4.35 and Ch.4
27: 4.31 Special Values and Limits
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4.31.1
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- Symbols:
- : hyperbolic sine function and : complex variable
- Permalink:
- http://dlmf.nist.gov/4.31.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.31 and Ch.4
4.31.2
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- Symbols:
- : hyperbolic tangent function and : complex variable
- Permalink:
- http://dlmf.nist.gov/4.31.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.31 and Ch.4
4.31.3
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- Symbols:
- : hyperbolic cosine function and : complex variable
- Permalink:
- http://dlmf.nist.gov/4.31.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.31 and Ch.4
28: 7.10 Derivatives
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7.10.1
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- Symbols:
- : Hermite polynomial, : the ratio of the circumference of a circle to its diameter, : derivative of with respect to , : error function, : base of natural logarithm, : complex variable and : nonnegative integer
- A&S Ref:
- 7.1.19
- Permalink:
- http://dlmf.nist.gov/7.10.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.10 and Ch.7
7.10.2
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : Faddeeva (or Faddeyeva) function, : imaginary unit and : complex variable
- A&S Ref:
- 7.1.20
- Permalink:
- http://dlmf.nist.gov/7.10.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.10 and Ch.7
7.10.3
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- Symbols:
- : Faddeeva (or Faddeyeva) function, : complex variable and : nonnegative integer
- A&S Ref:
- 7.1.20
- Permalink:
- http://dlmf.nist.gov/7.10.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.10 and Ch.7
29: 23.19 Interrelations
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23.19.1
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- Symbols:
- : Dedekind’s eta function (or Dedekind modular function), : elliptic modular function and : complex variable
- Permalink:
- http://dlmf.nist.gov/23.19.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §23.19 and Ch.23
23.19.2
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- Symbols:
- : Klein’s complete invariant, : elliptic modular function and : complex variable
- Permalink:
- http://dlmf.nist.gov/23.19.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §23.19 and Ch.23
23.19.3
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- Symbols:
- : Klein’s complete invariant, : Weierstrass lattice invariants , , : lattice and : complex variable
- Permalink:
- http://dlmf.nist.gov/23.19.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §23.19 and Ch.23
23.19.4
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- Symbols:
- : Dedekind’s eta function (or Dedekind modular function), : the ratio of the circumference of a circle to its diameter, : discriminant and : complex variable
- Referenced by:
- §23.19
- Permalink:
- http://dlmf.nist.gov/23.19.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §23.19 and Ch.23