functions of matrix argument
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11: 35.12 Software
Koev and Edelman (2006). Computation of hypergeometric functions of matrix argument in MATLAB.
12: Errata
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Poor spacing in math was corrected in several chapters.

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In Section 1.13, there were several modifications. In Equation (1.13.4), the determinant form of the twoargument Wronskian
1.13.4$$\mathcal{W}\left\{{w}_{1}(z),{w}_{2}(z)\right\}=det\left[\begin{array}{cc}\hfill {w}_{1}(z)\hfill & \hfill {w}_{2}(z)\hfill \\ \hfill {w}_{1}^{\prime}(z)\hfill & \hfill {w}_{2}^{\prime}(z)\hfill \end{array}\right]={w}_{1}(z){w}_{2}^{\prime}(z){w}_{2}(z){w}_{1}^{\prime}(z)$$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 $n$argument Wronskian is given by $\mathcal{W}\left\{{w}_{1}(z),\mathrm{\dots},{w}_{n}(z)\right\}=det\left[{w}_{k}^{(j1)}(z)\right]$, where $1\le j,k\le n$. Immediately below Equation (1.13.4), a sentence was added giving the definition of the $n$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 $n$thorder differential equations. A reference to Ince (1926, §5.2) was added.

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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 7542019 FloatingPoint Arithmetic Standard IEEE (2019). In the new standard, single, double and quad floatingpoint precisions are replaced with new standard names of binary32, binary64 and binary128. Figure 3.1.1 has been expanded to include the binary128 floatingpoint 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.

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In Equation (35.7.3), originally the matrix in the argument of the Gaussian hypergeometric function of matrix argument ${}_{2}F_{1}$ was written with round brackets. This matrix has been rewritten with square brackets to be consistent with the rest of the DLMF.

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The overloaded operator $\equiv $ is now more clearly separated (and linked) to two distinct cases: equivalence by definition (in §§1.4(ii), 1.4(v), 2.7(i), 2.10(iv), 3.1(i), 3.1(iv), 4.18, 9.18(ii), 9.18(vi), 9.18(vi), 18.2(iv), 20.2(iii), 20.7(vi), 23.20(ii), 25.10(i), 26.15, 31.17(i)); and modular equivalence (in §§24.10(i), 24.10(ii), 24.10(iii), 24.10(iv), 24.15(iii), 24.19(ii), 26.14(i), 26.21, 27.2(i), 27.8, 27.9, 27.11, 27.12, 27.14(v), 27.14(vi), 27.15, 27.16, 27.19).
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In Chapter 35 Functions of Matrix Argument, the generalized hypergeometric function of matrix argument ${}_{p}F_{q}({a}_{1},\mathrm{\dots},{a}_{p};{b}_{1},\mathrm{\dots},{b}_{q};\mathbf{T})$, was labeled inadvertently as its single variable counterpart ${}_{p}F_{q}({a}_{1},\mathrm{\dots},{a}_{p};{b}_{1},\mathrm{\dots},{b}_{q};\mathbf{T})$. Furthermore, the Jacobi function of matrix argument ${P}_{\nu}^{(\gamma ,\delta )}\left(\mathbf{T}\right)$, and the Laguerre function of matrix argument ${L}_{\nu}^{(\gamma )}\left(\mathbf{T}\right)$, were also labeled inadvertently (and incorrectly) in terms of the single variable counterparts given by ${P}_{\nu}^{(\gamma ,\delta )}\left(\mathbf{T}\right)$, and ${L}_{\nu}^{(\gamma )}\left(\mathbf{T}\right)$. In order to resolve these inconsistencies, these functions now link correctly to their respective definitions.