for ratios
(0.003 seconds)
31—40 of 415 matching pages
31: 28.22 Connection Formulas
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28.22.1
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- Symbols:
- : Mathieu function, : the ratio of the circumference of a circle to its diameter, : modified Mathieu function, : radial Mathieu function, : integer, : parameter, : complex variable and , : joining factors
- A&S Ref:
- 20.6.15 (in different form)
- Permalink:
- http://dlmf.nist.gov/28.22.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.22(i), §28.22 and Ch.28
28.22.2
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- Symbols:
- : Mathieu function, : the ratio of the circumference of a circle to its diameter, : radial Mathieu function, : modified Mathieu function, : integer, : parameter, : complex variable and , : joining factors
- Permalink:
- http://dlmf.nist.gov/28.22.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.22(i), §28.22 and Ch.28
28.22.5
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- Symbols:
- : Mathieu function, : the ratio of the circumference of a circle to its diameter, : integer, : parameter, , : joining factors and : Fourier coefficient
- Permalink:
- http://dlmf.nist.gov/28.22.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.22(i), §28.22 and Ch.28
28.22.6
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- Symbols:
- : Mathieu function, : the ratio of the circumference of a circle to its diameter, : integer, : parameter, , : joining factors and : Fourier coefficient
- Permalink:
- http://dlmf.nist.gov/28.22.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.22(i), §28.22 and Ch.28
28.22.7
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- Symbols:
- : Mathieu function, : the ratio of the circumference of a circle to its diameter, : integer, : parameter, , : joining factors and : Fourier coefficient
- Permalink:
- http://dlmf.nist.gov/28.22.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.22(i), §28.22 and Ch.28
32: 28.29 Definitions and Basic Properties
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28.29.2
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : complex variable and : function
- Permalink:
- http://dlmf.nist.gov/28.29.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.29(i), §28.29 and Ch.28
28.29.3
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : differential of , : integral, : complex variable and : function
- Permalink:
- http://dlmf.nist.gov/28.29.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.29(i), §28.29 and Ch.28
28.29.7
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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 : Mathieu’s equation solution
- Referenced by:
- §28.29(ii)
- Permalink:
- http://dlmf.nist.gov/28.29.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.29(ii), §28.29 and Ch.28
28.29.11
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : complex variable, : complex parameter, : Mathieu’s equation solution and : constant
- Permalink:
- http://dlmf.nist.gov/28.29.E11
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.29(ii), §28.29 and Ch.28
28.29.13
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : cosine function, : complex variable, : complex parameter and : Mathieu’s equation solution
- Permalink:
- http://dlmf.nist.gov/28.29.E13
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.29(ii), §28.29 and Ch.28
33: 7.11 Relations to Other Functions
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7.11.1
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : error function, : incomplete gamma function and : complex variable
- Permalink:
- http://dlmf.nist.gov/7.11.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.11, §7.11 and Ch.7
7.11.2
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : complementary error function, : incomplete gamma function and : complex variable
- Referenced by:
- §7.12(i)
- Permalink:
- http://dlmf.nist.gov/7.11.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.11, §7.11 and Ch.7
7.11.3
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : complementary error function, : generalized exponential integral and : complex variable
- Referenced by:
- §7.12(i)
- Permalink:
- http://dlmf.nist.gov/7.11.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.11, §7.11 and Ch.7
7.11.4
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- Symbols:
- : Kummer confluent hypergeometric function, : the ratio of the circumference of a circle to its diameter, : error function, : base of natural logarithm and : complex variable
- A&S Ref:
- 7.1.21
- Permalink:
- http://dlmf.nist.gov/7.11.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.11, §7.11 and Ch.7
7.11.5
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- Symbols:
- : Kummer confluent hypergeometric function, : the ratio of the circumference of a circle to its diameter, : complementary error function, : base of natural logarithm and : complex variable
- Referenced by:
- §7.11
- Permalink:
- http://dlmf.nist.gov/7.11.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §7.11, §7.11 and Ch.7
34: 9.5 Integral Representations
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9.5.1
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- Symbols:
- : Airy function, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : integral and : real variable
- Source:
- Olver (1997b, p. 53)
- A&S Ref:
- 10.4.32 (in different form)
- Permalink:
- http://dlmf.nist.gov/9.5.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §9.5(i), §9.5 and Ch.9
9.5.2
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- Symbols:
- : Airy function, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : integral and : real variable
- Source:
- Olver (1997b, p. 103)
- A&S Ref:
- 10.4.32 (in different form)
- Permalink:
- http://dlmf.nist.gov/9.5.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §9.5(i), §9.5 and Ch.9
9.5.4
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- Symbols:
- : Airy function, : the ratio of the circumference of a circle to its diameter, : differential of , : exponential function, : base of natural logarithm, : imaginary unit, : integral and : complex variable
- Source:
- Olver (1997b, p. 53)
- Referenced by:
- §36.2(ii), §9.14, §9.17(iii), (9.5.5)
- Permalink:
- http://dlmf.nist.gov/9.5.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §9.5(ii), §9.5 and Ch.9
9.5.6
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- Symbols:
- : Airy function, : the ratio of the circumference of a circle to its diameter, : differential of , : exponential function, : integral, : phase and : complex variable
- Source:
- Reid (1995, (5.4), p. 170, with change of variable and using analytic continuation to complex )
- Referenced by:
- Erratum (V1.0.15) for Equation (9.5.6)
- Permalink:
- http://dlmf.nist.gov/9.5.E6
- Encodings:
- pMML, png, TeX
- Clarification (effective with 1.0.15):
- The validity constraint was added.
- See also:
- Annotations for §9.5(ii), §9.5 and Ch.9
9.5.7
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- Symbols:
- : Airy function, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : exponential function, : base of natural logarithm, : integral, : phase, : complex variable and : change of variable
- Source:
- Copson (1963, (2.1))
- Referenced by:
- §9.5(ii)
- Permalink:
- http://dlmf.nist.gov/9.5.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §9.5(ii), §9.5 and Ch.9
35: 24.8 Series Expansions
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24.8.1
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- Symbols:
- : Bernoulli polynomials, : the ratio of the circumference of a circle to its diameter, : cosine function, : factorial (as in ), : integer, : integer and : real or complex
- A&S Ref:
- 23.1.18
- Referenced by:
- §24.8(i)
- Permalink:
- http://dlmf.nist.gov/24.8.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §24.8(i), §24.8 and Ch.24
24.8.2
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- Symbols:
- : Bernoulli polynomials, : the ratio of the circumference of a circle to its diameter, : factorial (as in ), : sine function, : integer, : integer and : real or complex
- A&S Ref:
- 23.1.17
- Permalink:
- http://dlmf.nist.gov/24.8.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §24.8(i), §24.8 and Ch.24
24.8.3
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- Symbols:
- : Bernoulli polynomials, : the ratio of the circumference of a circle to its diameter, : base of natural logarithm, : factorial (as in ), : imaginary unit, : integer, : integer and : real or complex
- Referenced by:
- §24.8(i)
- Permalink:
- http://dlmf.nist.gov/24.8.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §24.8(i), §24.8 and Ch.24
24.8.6
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- Symbols:
- : Bernoulli numbers, : the ratio of the circumference of a circle to its diameter, : base of natural logarithm, : integer and : integer
- Referenced by:
- §24.8(ii)
- Permalink:
- http://dlmf.nist.gov/24.8.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §24.8(ii), §24.8 and Ch.24
24.8.7
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- Symbols:
- : Bernoulli numbers, : the ratio of the circumference of a circle to its diameter, : base of natural logarithm, : integer and : integer
- Permalink:
- http://dlmf.nist.gov/24.8.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §24.8(ii), §24.8 and Ch.24
36: 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
28.19.3
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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
37: 28.30 Expansions in Series of Eigenfunctions
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28.30.2
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- Symbols:
- : Kronecker delta, : the ratio of the circumference of a circle to its diameter, : differential of , : integral, : integer, : integer, : real variable and : Mathieu’s equation solution
- Permalink:
- http://dlmf.nist.gov/28.30.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.30(i), §28.30 and Ch.28
28.30.4
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : differential of , : integral, : integer, : real variable and : Mathieu’s equation solution
- Permalink:
- http://dlmf.nist.gov/28.30.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.30(i), §28.30 and Ch.28
38: 5.16 Sums
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5.16.1
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : psi (or digamma) function and : nonnegative integer
- Permalink:
- http://dlmf.nist.gov/5.16.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §5.16 and Ch.5
39: 10.67 Asymptotic Expansions for Large Argument
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10.67.1
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- Symbols:
- : Kelvin function, : Poincaré asymptotic expansion, : the ratio of the circumference of a circle to its diameter, : cosine function, : base of natural logarithm, : nonnegative integer, : real variable, : complex parameter and : polynomial coefficient
- A&S Ref:
- 9.10.3, 9.10.5--9.10.7 (modified)
- Referenced by:
- §10.61(v), §10.67(ii), §10.68(iii)
- Permalink:
- http://dlmf.nist.gov/10.67.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.67(i), §10.67 and Ch.10
10.67.2
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- Symbols:
- : Kelvin function, : Poincaré asymptotic expansion, : the ratio of the circumference of a circle to its diameter, : base of natural logarithm, : sine function, : nonnegative integer, : real variable, : complex parameter and : polynomial coefficient
- A&S Ref:
- 9.10.4, 9.10.5--9.10.7 (modified)
- Referenced by:
- §10.61(v)
- Permalink:
- http://dlmf.nist.gov/10.67.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.67(i), §10.67 and Ch.10
10.67.5
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- Symbols:
- : Kelvin function, : Poincaré asymptotic expansion, : the ratio of the circumference of a circle to its diameter, : cosine function, : base of natural logarithm, : nonnegative integer, : real variable, : complex parameter and : polynomial coefficient
- A&S Ref:
- §9.10 (modified)
- Permalink:
- http://dlmf.nist.gov/10.67.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.67(i), §10.67 and Ch.10
10.67.6
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- Symbols:
- : Kelvin function, : Poincaré asymptotic expansion, : the ratio of the circumference of a circle to its diameter, : base of natural logarithm, : sine function, : nonnegative integer, : real variable, : complex parameter and : polynomial coefficient
- A&S Ref:
- §9.10 (modified)
- Permalink:
- http://dlmf.nist.gov/10.67.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.67(i), §10.67 and Ch.10
10.67.9
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- Symbols:
- : Kelvin function, : Kelvin function, : Poincaré asymptotic expansion, : the ratio of the circumference of a circle to its diameter, : base of natural logarithm and : real variable
- A&S Ref:
- 9.10.27
- Permalink:
- http://dlmf.nist.gov/10.67.E9
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.67(ii), §10.67 and Ch.10
40: 33.18 Limiting Forms for Large
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