reciprocity law
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11—20 of 28 matching pages
11: 5.7 Series Expansions
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§5.7(i) Maclaurin and Taylor Series
…12: 23.20 Mathematical Applications
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►In terms of the addition law can be expressed , ; otherwise , where
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23.20.4
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►The addition law states that to find the sum of two points, take the third intersection with of the chord joining them (or the tangent if they coincide); then its reflection in the -axis gives the required sum.
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13: 5.8 Infinite Products
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5.8.3
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14: 5.19 Mathematical Applications
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►Many special functions can be represented as a Mellin–Barnes
integral, that is, an integral of a product of gamma functions, reciprocals of gamma functions, and a power of , the integration contour being doubly-infinite and eventually parallel to the imaginary axis at both ends.
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15: 5.23 Approximations
16: 19.31 Probability Distributions
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and occur as the expectation values, relative to a normal probability distribution in or , of the square root or reciprocal square root of a quadratic form.
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17: 22.18 Mathematical Applications
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►For any two points and on this curve, their sum
, always a third point on the curve, is defined by the Jacobi–Abel addition law
…With the identification , , the addition law (22.18.8) is transformed into the addition theorem (22.8.1); see Akhiezer (1990, pp. 42, 45, 73–74) and McKean and Moll (1999, §§2.14, 2.16).
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18: 19.7 Connection Formulas
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Reciprocal-Modulus Transformation
…19: Bibliography N
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Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal.
Proc. Roy. Soc. Edinburgh Sect. A 145 (3), pp. 571–596.
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