cosine function
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21—30 of 282 matching pages
21: 14.19 Toroidal (or Ring) Functions
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14.19.4
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- Symbols:
- : gamma function, : associated Legendre function of the first kind, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : hyperbolic cosine function, : hyperbolic sine function, : integral, : sine function, : nonnegative integer, : nonnegative integer and : variable
- A&S Ref:
- 8.11.2
- Permalink:
- http://dlmf.nist.gov/14.19.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.19(iii), §14.19 and Ch.14
14.19.5
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- Symbols:
- : gamma function, : Olver’s associated Legendre function, : differential of , : hyperbolic cosine function, : hyperbolic sine function, : integral, : nonnegative integer, : nonnegative integer and : variable
- A&S Ref:
- 8.11.4 (modified and corrected)
- Permalink:
- http://dlmf.nist.gov/14.19.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.19(iii), §14.19 and Ch.14
14.19.6
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ⓘ
- Symbols:
- : gamma function, : Olver’s associated Legendre function, : the ratio of the circumference of a circle to its diameter, : cosine function, : hyperbolic cosine function, : hyperbolic sine function, : real part, : nonnegative integer, : general order and : variable
- Permalink:
- http://dlmf.nist.gov/14.19.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.19(iv), §14.19 and Ch.14
14.19.7
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ⓘ
- Symbols:
- : gamma function, : associated Legendre function of the first kind, : Olver’s associated Legendre function, : the ratio of the circumference of a circle to its diameter, : hyperbolic cosine function, : hyperbolic cotangent function, : hyperbolic sine function, : nonnegative integer, : nonnegative integer and : variable
- Permalink:
- http://dlmf.nist.gov/14.19.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.19(v), §14.19 and Ch.14
14.19.8
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- Symbols:
- : gamma function, : associated Legendre function of the first kind, : Olver’s associated Legendre function, : the ratio of the circumference of a circle to its diameter, : hyperbolic cosine function, : hyperbolic cotangent function, : hyperbolic sine function, : nonnegative integer, : nonnegative integer and : variable
- Permalink:
- http://dlmf.nist.gov/14.19.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.19(v), §14.19 and Ch.14
22: 24.7 Integral Representations
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24.7.7
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- Symbols:
- : Bernoulli polynomials, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : base of natural logarithm, : hyperbolic cosine function, : integral, : integer, : real or complex and : real or complex
- Permalink:
- http://dlmf.nist.gov/24.7.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §24.7(ii), §24.7 and Ch.24
24.7.8
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ⓘ
- Symbols:
- : Bernoulli polynomials, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : hyperbolic cosine function, : integral, : sine function, : integer, : real or complex and : real or complex
- Permalink:
- http://dlmf.nist.gov/24.7.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §24.7(ii), §24.7 and Ch.24
24.7.9
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- Symbols:
- : Euler polynomials, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : hyperbolic cosine function, : integral, : sine function, : integer, : real or complex and : real or complex
- Permalink:
- http://dlmf.nist.gov/24.7.E9
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §24.7(ii), §24.7 and Ch.24
24.7.10
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- Symbols:
- : Euler polynomials, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : hyperbolic cosine function, : hyperbolic sine function, : integral, : integer, : real or complex and : real or complex
- Permalink:
- http://dlmf.nist.gov/24.7.E10
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §24.7(ii), §24.7 and Ch.24
23: 4.17 Special Values and Limits
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4.17.3
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- Symbols:
- : cosine function and : complex variable
- Permalink:
- http://dlmf.nist.gov/4.17.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.17 and Ch.4
24: 28.11 Expansions in Series of Mathieu Functions
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28.11.4
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- Symbols:
- : Mathieu function, : cosine function, : integer, : parameter, : integer, : complex variable and : Fourier coefficient
- Permalink:
- http://dlmf.nist.gov/28.11.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.11, §28.11 and Ch.28
28.11.5
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- Symbols:
- : Mathieu function, : cosine function, : integer, : parameter, : integer, : complex variable and : Fourier coefficient
- Permalink:
- http://dlmf.nist.gov/28.11.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.11, §28.11 and Ch.28
25: 4.34 Derivatives and Differential Equations
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4.34.1
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- Symbols:
- : derivative of with respect to , : hyperbolic cosine function, : hyperbolic sine function and : complex variable
- A&S Ref:
- 4.5.71
- Permalink:
- http://dlmf.nist.gov/4.34.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.34 and Ch.4
4.34.2
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- Symbols:
- : derivative of with respect to , : hyperbolic cosine function, : hyperbolic sine function and : complex variable
- A&S Ref:
- 4.5.72
- Permalink:
- http://dlmf.nist.gov/4.34.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.34 and Ch.4
4.34.11
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- Symbols:
- : hyperbolic cosine function, : hyperbolic sine function, : real or complex constant, : complex variable, : solution, : arbitrary constant and : arbitrary constant
- Permalink:
- http://dlmf.nist.gov/4.34.E11
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.34 and Ch.4
4.34.13
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- Symbols:
- : hyperbolic cosine function, : real or complex constant, : complex variable, : solution and : arbitrary constant
- Permalink:
- http://dlmf.nist.gov/4.34.E13
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.34 and Ch.4
26: 28.23 Expansions in Series of Bessel Functions
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28.23.2
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- Symbols:
- : Mathieu function, : hyperbolic cosine function, : modified Mathieu function, : parameter, : integer, : integer, : complex variable, : complex parameter, : coefficients and : cylinder functions
- Permalink:
- http://dlmf.nist.gov/28.23.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.23 and Ch.28
28.23.3
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- Symbols:
- : Mathieu function, : hyperbolic cosine function, : hyperbolic tangent function, : imaginary unit, : modified Mathieu function, : parameter, : integer, : integer, : complex variable, : complex parameter, : coefficients and : cylinder functions
- Permalink:
- http://dlmf.nist.gov/28.23.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.23 and Ch.28
28.23.6
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- Symbols:
- : Mathieu function, : hyperbolic cosine function, : radial Mathieu function, : integer, : parameter, : integer, : complex variable, : cylinder functions and : Fourier coefficient
- A&S Ref:
- 20.6.12
- Referenced by:
- §28.23
- Permalink:
- http://dlmf.nist.gov/28.23.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.23 and Ch.28
28.23.8
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- Symbols:
- : Mathieu function, : hyperbolic cosine function, : radial Mathieu function, : integer, : parameter, : integer, : complex variable, : cylinder functions and : Fourier coefficient
- Permalink:
- http://dlmf.nist.gov/28.23.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.23 and Ch.28
28.23.10
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- Symbols:
- : Mathieu function, : hyperbolic cosine function, : hyperbolic tangent function, : radial Mathieu function, : integer, : parameter, : integer, : complex variable, : cylinder functions and : Fourier coefficient
- Permalink:
- http://dlmf.nist.gov/28.23.E10
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.23 and Ch.28
27: 17.3 -Elementary and -Special Functions
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-Cosine Functions
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17.3.5
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- Defines:
- : -cosine function
- Symbols:
- : imaginary unit, : -Pochhammer symbol (or -shifted factorial), : -exponential function, : complex base, : nonnegative integer and : real variable
- Permalink:
- http://dlmf.nist.gov/17.3.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §17.3(i), §17.3(i), §17.3 and Ch.17
17.3.6
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- Defines:
- : -cosine function
- Symbols:
- : imaginary unit, : -exponential function, : -Pochhammer symbol (or -shifted factorial), : complex base, : nonnegative integer and : real variable
- Permalink:
- http://dlmf.nist.gov/17.3.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §17.3(i), §17.3(i), §17.3 and Ch.17
28: 6.7 Integral Representations
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6.7.10
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : complementary exponential integral, : cosine function, : cosine integral, : differential of , : base of natural logarithm, : integral, : sine function and : complex variable
- A&S Ref:
- 5.2.11 (modified form of)
- Permalink:
- http://dlmf.nist.gov/6.7.E10
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §6.7(ii), §6.7 and Ch.6
6.7.11
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- Symbols:
- : complementary exponential integral, : cosine function, : cosine integral, : differential of , : element of, : base of natural logarithm, : imaginary unit, : integral, : real part and : real line
- A&S Ref:
- 5.2.33 (modified form of)
- Permalink:
- http://dlmf.nist.gov/6.7.E11
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §6.7(ii), §6.7 and Ch.6
§6.7(iii) Auxiliary Functions
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6.7.15
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- Symbols:
- : cosine function, : differential of , : integral, : modified Bessel function of the second kind, : auxiliary function for sine and cosine integrals and : complex variable
- Referenced by:
- §6.7(iii)
- Permalink:
- http://dlmf.nist.gov/6.7.E15
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §6.7(iii), §6.7 and Ch.6
6.7.16
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- Symbols:
- : differential of , : integral, : modified Bessel function of the second kind, : sine function, : auxiliary function for sine and cosine integrals and : complex variable
- Referenced by:
- §6.7(iii)
- Permalink:
- http://dlmf.nist.gov/6.7.E16
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §6.7(iii), §6.7 and Ch.6
29: 14.5 Special Values
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14.5.11
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- Symbols:
- : Ferrers function of the first kind, : the ratio of the circumference of a circle to its diameter, : cosine function, : sine function, : general degree and : variable
- A&S Ref:
- 8.6.12
- Permalink:
- http://dlmf.nist.gov/14.5.E11
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.5(iii), §14.5 and Ch.14
14.5.14
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- Symbols:
- : Ferrers function of the second kind, : the ratio of the circumference of a circle to its diameter, : cosine function, : sine function, : general degree and : variable
- A&S Ref:
- 8.6.15 (corrected)
- Referenced by:
- Erratum (V1.0.16) for Equation (14.5.14)
- Permalink:
- http://dlmf.nist.gov/14.5.E14
- Encodings:
- pMML, png, TeX
- Errata (effective with 1.0.16):
-
Originally this equation was incorrect because of a minus sign in front of the right-hand side.
Reported 2017-04-10 by André Greiner-Petter
- See also:
- Annotations for §14.5(iii), §14.5 and Ch.14
14.5.17
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- Symbols:
- : gamma function, : Olver’s associated Legendre function, : the ratio of the circumference of a circle to its diameter, : exponential function, : hyperbolic cosine function, : hyperbolic sine function, : general degree and : variable
- A&S Ref:
- 8.6.10 (corrected) 8.6.11 (corrected)
- Permalink:
- http://dlmf.nist.gov/14.5.E17
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.5(iii), §14.5 and Ch.14
14.5.18
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- Symbols:
- : gamma function, : Ferrers function of the first kind, : cosine function, : sine function, : general degree and : variable
- A&S Ref:
- 8.6.17
- Permalink:
- http://dlmf.nist.gov/14.5.E18
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.5(iv), §14.5 and Ch.14
14.5.23
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- Symbols:
- : Legendre’s complete elliptic integral of the first kind, : cosine function, : Ferrers function of the second kind and : variable
- A&S Ref:
- 8.13.10 (in slightly different form)
- Permalink:
- http://dlmf.nist.gov/14.5.E23
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.5(v), §14.5 and Ch.14
30: 28.10 Integral Equations
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28.10.1
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- Symbols:
- : Mathieu function, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : integral, : parameter, : integer, : complex variable and : Fourier coefficient
- A&S Ref:
- 20.7.20 (in different form)
- Permalink:
- http://dlmf.nist.gov/28.10.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.10(i), §28.10 and Ch.28
28.10.2
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- Symbols:
- : Mathieu function, : the ratio of the circumference of a circle to its diameter, : differential of , : hyperbolic cosine function, : integral, : sine function, : parameter, : integer, : complex variable and : Fourier coefficient
- A&S Ref:
- 20.7.21 (in different form)
- Permalink:
- http://dlmf.nist.gov/28.10.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.10(i), §28.10 and Ch.28
28.10.3
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- Symbols:
- : Mathieu function, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : integral, : sine function, : parameter, : integer, : complex variable and : Fourier coefficient
- A&S Ref:
- 20.7.20 (in different form)
- Permalink:
- http://dlmf.nist.gov/28.10.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.10(i), §28.10 and Ch.28
28.10.4
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- Symbols:
- : Mathieu function, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : hyperbolic cosine function, : integral, : sine function, : parameter, : integer, : complex variable and : Fourier coefficient
- A&S Ref:
- 20.7.21 (in different form)
- Permalink:
- http://dlmf.nist.gov/28.10.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.10(i), §28.10 and Ch.28
28.10.10
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- Symbols:
- : Bessel function of the first kind, : Mathieu function, : eigenvalues of Mathieu equation, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : integral, : parameter, : integer and : fundamental solution
- Permalink:
- http://dlmf.nist.gov/28.10.E10
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.10(ii), §28.10 and Ch.28