scaling of variables and parameters
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1—10 of 27 matching pages
1: 33.22 Particle Scattering and Atomic and Molecular Spectra
2: 36.5 Stokes Sets
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βΊ
36.5.8
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βΊ
β
- Symbols:
- : sign of, : real parameter, : variable and : scaled coordinate
- Permalink:
- http://dlmf.nist.gov/36.5.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §36.5(ii), §36.5(ii), §36.5 and Ch.36
36.5.9
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β
- Symbols:
- : sign of, : real parameter, : variable and : scaled coordinate
- Referenced by:
- §36.5(ii)
- Permalink:
- http://dlmf.nist.gov/36.5.E9
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §36.5(ii), §36.5(ii), §36.5 and Ch.36
3: 15.12 Asymptotic Approximations
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15.12.5
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βΊ
β
- Symbols:
- : order not exceeding, : hyperbolic cotangent function, : hyperbolic sine function, : hyperbolic tangent function, : modified Bessel function of the first kind, or : Olver’s hypergeometric function, : complex variable, : real or complex parameter, : real or complex parameter, : real or complex parameter and : change of variable
- Permalink:
- http://dlmf.nist.gov/15.12.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §15.12(iii), §15.12 and Ch.15
15.12.9
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β
- Symbols:
- : Airy function, : order not exceeding, : the ratio of the circumference of a circle to its diameter, : base of natural logarithm, : imaginary unit, or : Olver’s hypergeometric function, : complex variable, : real or complex parameter, : real or complex parameter, : real or complex parameter, : change of variable, and : function
- Referenced by:
- §15.12(iii)
- Permalink:
- http://dlmf.nist.gov/15.12.E9
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §15.12(iii), §15.12 and Ch.15
4: 8.18 Asymptotic Expansions of
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βΊ
8.18.14
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β
- Symbols:
- : incomplete beta function, : Poincaré asymptotic expansion, : the ratio of the circumference of a circle to its diameter, : normalized incomplete gamma function, : scaled gamma function, : nonnegative integer, : parameter, : parameter, : variable, , : variable and : coefficients
- Permalink:
- http://dlmf.nist.gov/8.18.E14
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §8.18(ii), §8.18(ii), §8.18 and Ch.8
5: 15.7 Continued Fractions
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βΊ
15.7.1
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βΊ
β
- Symbols:
- or : Olver’s hypergeometric function, : complex variable, : real or complex parameter, : real or complex parameter, : real or complex parameter, : coefficient and : coefficient
- Permalink:
- http://dlmf.nist.gov/15.7.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §15.7 and Ch.15
15.7.3
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βΊ
β
- Symbols:
- or : Olver’s hypergeometric function, : complex variable, : real or complex parameter, : real or complex parameter, : real or complex parameter, : coefficient and : coefficient
- Permalink:
- http://dlmf.nist.gov/15.7.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §15.7 and Ch.15
15.7.5
…
β
- Symbols:
- or : Olver’s hypergeometric function, : real variable, : real variable, : complex variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Permalink:
- http://dlmf.nist.gov/15.7.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §15.7 and Ch.15
6: 15.15 Sums
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15.15.1
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β
- Symbols:
- : Pochhammer’s symbol (or shifted factorial), : factorial (as in ), or : Olver’s hypergeometric function, : nonnegative integer, : complex variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Referenced by:
- §15.19(i)
- Permalink:
- http://dlmf.nist.gov/15.15.E1
- Encodings:
- pMML, png, TeX
- Correction (effective with 1.1.2):
- The Pochhammer symbol now links to its definition.
- See also:
- Annotations for §15.15 and Ch.15
7: 15.2 Definitions and Analytical Properties
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15.2.2
,
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βΊ
β
- Defines:
- or : Olver’s hypergeometric function
- Symbols:
- : gamma function, : Pochhammer’s symbol (or shifted factorial), : factorial (as in ), or : scaled (or Olver’s) generalized hypergeometric function, : nonnegative integer, : complex variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Referenced by:
- §15.12(i), §16.2(v)
- Permalink:
- http://dlmf.nist.gov/15.2.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §15.2(i), §15.2 and Ch.15
15.2.3
.
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βΊ
β
- Symbols:
- : gamma function, : the ratio of the circumference of a circle to its diameter, : imaginary unit, or : Olver’s hypergeometric function, : real variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Referenced by:
- §15.2(i)
- Permalink:
- http://dlmf.nist.gov/15.2.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §15.2(i), §15.2 and Ch.15
15.2.3_5
.
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β
- Symbols:
- : gamma function, or : Gauss’ hypergeometric function, : Pochhammer’s symbol (or shifted factorial), : factorial (as in ), or : Olver’s hypergeometric function, : integer, : complex variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Referenced by:
- §15.2(ii), Erratum (V1.0.28) for Equations (15.2.3_5), (19.11.6_5)
- Permalink:
- http://dlmf.nist.gov/15.2.E3_5
- Encodings:
- pMML, png, TeX
- Clarification (effective with 1.0.28):
- This equation was given a number.
- See also:
- Annotations for §15.2(ii), §15.2 and Ch.15
8: 15.1 Special Notation
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15.1.2
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β
- Symbols:
- : gamma function, or : Gauss’ hypergeometric function, or : scaled (or Olver’s) generalized hypergeometric function, or : Olver’s hypergeometric function, : complex variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Permalink:
- http://dlmf.nist.gov/15.1.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §15.1 and Ch.15
9: 15.6 Integral Representations
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15.6.1
; .
βΊ
β
- Symbols:
- : gamma function, : the ratio of the circumference of a circle to its diameter, : differential of , : integral, : phase, : real part, or : Olver’s hypergeometric function, : complex variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Keywords:
- Mellin transform
- Referenced by:
- §15.19(iii), (15.4.34), §15.6, §15.6, Erratum (V1.0.23) for Equations (15.6.1)–(15.6.9), Erratum (V1.0.23) for Equations (15.6.1)–(15.6.9)
- Permalink:
- http://dlmf.nist.gov/15.6.E1
- Encodings:
- pMML, png, TeX
- Addition (effective with 1.0.23):
- The Olver hypergeometric function , previously omitted from the left-hand side to make the formula more concise, has been added. The constraint , originally mentioned in the text, has been directly added to the formula.
- See also:
- Annotations for §15.6 and Ch.15
15.6.2
; , .
βΊ
β
- Symbols:
- : gamma function, : the ratio of the circumference of a circle to its diameter, : differential of , : imaginary unit, : integral, : phase, : real part, or : Olver’s hypergeometric function, : complex variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Keywords:
- Mellin transform
- Referenced by:
- §15.6
- Permalink:
- http://dlmf.nist.gov/15.6.E2
- Encodings:
- pMML, png, TeX
- Addition (effective with 1.0.23):
- The Olver hypergeometric function , previously omitted from the left-hand side to make the formula more concise, has been added. The constraint , originally mentioned in the text, has been directly added to the formula.
- See also:
- Annotations for §15.6 and Ch.15
15.6.2_5
; .
…
βΊ
β
- Symbols:
- : gamma function, : the ratio of the circumference of a circle to its diameter, : differential of , : integral, : phase, : real part, or : Olver’s hypergeometric function, : complex variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Keywords:
- Mellin transform
- Referenced by:
- §15.6, Erratum (V1.1.5) for Additions
- Permalink:
- http://dlmf.nist.gov/15.6.E2_5
- Encodings:
- pMML, png, TeX
- Addition (effective with 1.1.5):
- This equation was added.
- See also:
- Annotations for §15.6 and Ch.15
15.6.6
; .
…
βΊ
β
- Symbols:
- : gamma function, : the ratio of the circumference of a circle to its diameter, : differential of , : imaginary unit, : integral, : phase, or : Olver’s hypergeometric function, : complex variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- A&S Ref:
- 15.3.2 (modified)
- Referenced by:
- §15.6, §15.6, Erratum (V1.0.23) for Equations (15.6.1)–(15.6.9)
- Permalink:
- http://dlmf.nist.gov/15.6.E6
- Encodings:
- pMML, png, TeX
- Addition (effective with 1.0.23):
- The Olver hypergeometric function , previously omitted from the left-hand side to make the formula more concise, has been added. The constraint , originally mentioned in the text, has been directly added to the formula.
- See also:
- Annotations for §15.6 and Ch.15
15.6.8
; .
…
β
- Symbols:
- : gamma function, : the ratio of the circumference of a circle to its diameter, : differential of , : integral, : phase, : real part, or : Olver’s hypergeometric function, : complex variable, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Keywords:
- Mellin transform
- Proof sketch:
- Follows from (15.6.9) with .
- Referenced by:
- (15.6.9), §15.6, §15.6, §15.6, §18.17(iv), Erratum (V1.0.14) for Equation (15.6.8), Erratum (V1.0.14) for Equation (15.6.8)
- Permalink:
- http://dlmf.nist.gov/15.6.E8
- Encodings:
- pMML, png, TeX
- Addition (effective with 1.0.23):
- The Olver hypergeometric function , previously omitted from the left-hand side to make the formula more concise, has been added. The constraint , originally mentioned in the text, has been directly added to the formula.
- See also:
- Annotations for §15.6 and Ch.15
10: 15.14 Integrals
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βΊ
15.14.1
.
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β
- Symbols:
- : gamma function, : differential of , : integral, : real part, or : Olver’s hypergeometric function, : real variable, : nonnegative integer, : real or complex parameter, : real or complex parameter and : real or complex parameter
- Keywords:
- Mellin transform
- Referenced by:
- §15.14
- Permalink:
- http://dlmf.nist.gov/15.14.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §15.14 and Ch.15