Gaussian hypergeometric function
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1: 35.7 Gaussian Hypergeometric Function of Matrix Argument
§35.7 Gaussian Hypergeometric Function of Matrix Argument
►§35.7(i) Definition
… ►Jacobi Form
… ►Confluent Form
… ►Integral Representation
…2: 35.10 Methods of Computation
3: 35.9 Applications
§35.9 Applications
…4: 35.1 Special Notation
$a,b$  complex variables. 

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5: Bibliography H
6: 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.