Abel–Plana formula
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41: 3.4 Differentiation
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Two-Point Formula
… ►Three-Point Formula
… ►Four-Point Formula
… ►Five-Point Formula
… ►Six-Point Formula
…42: 36.5 Stokes Sets
43: 10.4 Connection Formulas
§10.4 Connection Formulas
…44: 6.18 Methods of Computation
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►Also, other ranges of can be covered by use of the continuation formulas of §6.4.
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►For example, the Gauss–Laguerre formula (§3.5(v)) can be applied to (6.2.2); see Todd (1954) and Tseng and Lee (1998).
For an application of the Gauss–Legendre formula (§3.5(v)) see Tooper and Mark (1968).
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45: About MathML
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►MathML allows us to present the mathematics independent on your screen size and resolution, enabling adjustment to enlarge or shrink formula, as well as providing opportunities for making the material accessible for those with disabilities.
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46: Foreword
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►In 1964 the National Institute of Standards and Technology11
1
Then known as
the National Bureau of Standards. published the Handbook of
Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by Milton Abramowitz and Irene A.
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47: Preface
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►The project had two equally important goals: to develop an authoritative replacement for the highly successful Handbook
of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, published in 1964 by the National Bureau of Standards (M.
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►All of the mathematical information contained in the Handbook is also contained in the DLMF, along with additional features such as more graphics, expanded tables, and higher members of some families of formulas; in consequence, in the Handbook there are occasional gaps in the numbering sequences of equations, tables, and figures.
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►Among these capabilities are: a facility to allow users to download LaTeX and MathML encodings of every formula into document processors and software packages (eventually, a fully semantic downloading capability may be possible); a search engine that allows users to locate formulas based on queries expressed in mathematical notation; and user-manipulable 3-dimensional color graphics.
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48: 8.24 Physical Applications
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►The function appears in: Monte Carlo sampling in statistical mechanics (Kofke (2004)); analysis of packings of soft or granular objects (Prellberg and Owczarek (1995)); growth formulas in cosmology (Hamilton (2001)).
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