fractional derivatives
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1: 1.15 Summability Methods
§1.15(vii) Fractional Derivatives
… ►2: 12.1 Special Notation
3: Errata

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A number of changes were made with regard to fractional integrals and derivatives. In §1.15(vi) a reference to Miller and Ross (1993) was added, the fractional integral operator of order $\alpha $ was more precisely identified as the RiemannLiouville fractional integral operator of order $\alpha $, and a paragraph was added below (1.15.50) to generalize (1.15.47). In §1.15(vii) the sentence defining the fractional derivative was clarified. In §2.6(iii) the identification of the RiemannLiouville fractional integral operator was made consistent with §1.15(vi).

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Changes to §8.18(ii)–§8.11(v): A sentence was added in §8.18(ii) to refer to Nemes and Olde Daalhuis (2016). Originally §8.11(iii) was applicable for real variables $a$ and $x=\lambda a$. It has been extended to allow for complex variables $a$ and $z=\lambda a$ (and we have replaced $x$ with $z$ in the subsection heading and in Equations (8.11.6) and (8.11.7)). Also, we have added two paragraphs after (8.11.9) to replace the original paragraph that appeared there. Furthermore, the interval of validity of (8.11.6) was increased from $$ to the sector $$, and the interval of validity of (8.11.7) was increased from $\lambda >1$ to the sector $\lambda >1$, $\mathrm{ph}a\le \frac{3\pi}{2}\delta $. A paragraph with reference to Nemes (2016) has been added in §8.11(v), and the sector of validity for (8.11.12) was increased from $\mathrm{ph}z\le \pi \delta $ to $\mathrm{ph}z\le 2\pi \delta $. Two new Subsections 13.6(vii), 13.18(vi), both entitled Coulomb Functions, were added to note the relationship of the Kummer and Whittaker functions to various forms of the Coulomb functions. A sentence was added in both §13.10(vi) and §13.23(v) noting that certain generalized orthogonality can be expressed in terms of Kummer functions.

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Four of the terms in (14.15.23) were rewritten for improved clarity.
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In applying changes in Version 1.0.12 to (16.15.3), an editing error was made; it has been corrected.
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Meta.Numerics (website) was added to the Software Index.