Mehler–Dirichlet formula
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31—40 of 257 matching pages
31: 5.5 Functional Relations
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§5.5(ii) Reflection
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5.5.3
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§5.5(iii) Multiplication
►Duplication Formula
… ►Gauss’s Multiplication Formula
…32: 24.6 Explicit Formulas
33: 24.16 Generalizations
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§24.16(ii) Character Analogs
►Let be a primitive Dirichlet character (see §27.8). Then is called the conductor of . … ►
24.16.11
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24.16.12
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34: 10.9 Integral Representations
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Mehler–Sonine and Related Integrals
…35: 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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36: 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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37: 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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38: 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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39: 3.5 Quadrature
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Gauss–Legendre Formula
… ►Gauss–Chebyshev Formula
… ►Gauss–Laguerre Formula
… ►a complex Gauss quadrature formula is available. …40: Errata
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Subsection 17.9(iii)
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Section 27.11
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Paragraph Inversion Formula (in §35.2)
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Equation (25.11.36)
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Usability
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The title of the paragraph which was previously “Gasper’s -Analog of Clausen’s Formula” has been changed to “Gasper’s -Analog of Clausen’s Formula (16.12.2)”.
The wording was changed to make the integration variable more apparent.
Additional keywords are being added to formulas (an ongoing project); these are visible in the associated ‘info boxes’ linked to the icons to the right of each formula, and provide better search capabilities.