Pfaff--Saalschutz formula
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11: 24.6 Explicit Formulas
12: 27.5 Inversion Formulas
§27.5 Inversion Formulas
… ►which, in turn, is the basis for the Möbius inversion formula relating sums over divisors: … ►Special cases of Möbius inversion pairs are: … ►Other types of Möbius inversion formulas include: …13: Possible Errors in DLMF
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►One source of confusion, rather than actual errors, are some new functions which differ from those in Abramowitz and Stegun (1964) by scaling, shifts or constraints on the domain; see the Info box (click or hover over the icon) for links to defining formula.
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14: 18.42 Software
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►A more complete list of available software for computing these functions, and for generating formulas symbolically, is found in the Software Index.
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15: Gergő Nemes
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►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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16: Wolter Groenevelt
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►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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17: 17.4 Basic Hypergeometric Functions
18: 3.5 Quadrature
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Gauss–Legendre Formula
… ►Gauss–Chebyshev Formula
… ►Gauss–Laguerre Formula
… ►a complex Gauss quadrature formula is available. …19: 25.4 Reflection Formulas
20: 2.2 Transcendental Equations
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►where and () is the coefficient of in the asymptotic expansion of (Lagrange’s formula for the reversion of
series).
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