quasi-addition formula
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11: 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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12: 3.5 Quadrature
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Gauss–Legendre Formula
… ►Gauss–Chebyshev Formula
… ►Gauss–Laguerre Formula
… ►a complex Gauss quadrature formula is available. …13: 25.4 Reflection Formulas
14: 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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15: 25.19 Tables
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Fletcher et al. (1962, §22.1) lists many sources for earlier tables of for both real and complex . §22.133 gives sources for numerical values of coefficients in the Riemann–Siegel formula, §22.15 describes tables of values of , and §22.17 lists tables for some Dirichlet -functions for real characters. For tables of dilogarithms, polylogarithms, and Clausen’s integral see §§22.84–22.858.
16: 29.20 Methods of Computation
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►Subsequently, formulas typified by (29.6.4) can be applied to compute the coefficients of the Fourier expansions of the corresponding Lamé functions by backward recursion followed by application of formulas typified by (29.6.5) and (29.6.6) to achieve normalization; compare §3.6.
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►§29.15(i) includes formulas for normalizing the eigenvectors.
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17: 14.28 Sums
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§14.28(ii) Heine’s Formula
…18: Need Help?
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Finding Things
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How do I search within DLMF? See Guide to Searching the DLMF.
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Links to definitions, keywords, annotations and other interesting information can be found in the Info boxes by clicking or hovering the mouse over the icon next to each formula, table, figure, and section heading.
19: 5.21 Methods of Computation
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►For the left half-plane we can continue the backward recurrence or make use of the reflection formula (5.5.3).
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20: 12.16 Mathematical Applications
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►PCFs are also used in integral transforms with respect to the parameter, and inversion formulas exist for kernels containing PCFs.
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