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§22.18(iv) Elliptic Curves and the Jacobi–Abel Addition Theorem… ►For any two points and on this curve, their sum , always a third point on the curve, is defined by the Jacobi–Abel addition law …a construction due to Abel; see Whittaker and Watson (1927, pp. 442, 496–497). …
Abel Summability… ►
Abel Means… ► is a harmonic function in polar coordinates ((1.9.27)), and … ►Here is the Abel (or Poisson) sum of , and has the series representation … ►
The first infinite integral in (2.10.2) converges.
Poor spacing in math was corrected in several chapters.
was added as an equality. In Paragraph Wronskian in §1.13(i), immediately below Equation (1.13.4), a sentence was added indicating that in general the -argument Wronskian is given by , where . Immediately below Equation (1.13.4), a sentence was added giving the definition of the -argument Wronskian. It is explained just above (1.13.5) that this equation is often referred to as Abel’s identity. Immediately below Equation (1.13.5), a sentence was added explaining how it generalizes for th-order differential equations. A reference to Ince (1926, §5.2) was added.
In Section 3.1, there were several modifications. In Paragraph IEEE Standard in §3.1(i), the description was modified to reflect the most recent IEEE 754-2019 Floating-Point Arithmetic Standard IEEE (2019). In the new standard, single, double and quad floating-point precisions are replaced with new standard names of binary32, binary64 and binary128. Figure 3.1.1 has been expanded to include the binary128 floating-point memory positions and the caption has been updated using the terminology of the 2019 standard. A sentence at the end of Subsection 3.1(ii) has been added referring readers to the IEEE Standards for Interval Arithmetic IEEE (2015, 2018). This was suggested by Nicola Torracca.
In Equation (35.7.3), originally the matrix in the argument of the Gaussian hypergeometric function of matrix argument was written with round brackets. This matrix has been rewritten with square brackets to be consistent with the rest of the DLMF.