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11: 3.8 Nonlinear Equations

… ►However, to guard against the accumulation of rounding errors, a final iteration for each zero should also be performed on the original polynomial $p(z)$. …

12: 35.7 Gaussian Hypergeometric Function of Matrix Argument

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35.7.3

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Symbols:

${}_p{}^{}F_q^{}(a_1,\mathrm{\dots },a_p;b_1,\mathrm{\dots },b_q;𝐓)$ or ${}_p{}^{}F_q^{}(\genfrac{}{}{0pt}{}{a_1,\mathrm{\dots },a_p}{b_1,\mathrm{\dots },b_q};𝐓)$: generalized hypergeometric function of matrix argument, ${\left(a\right)}_n$: Pochhammer’s symbol (or shifted factorial), $!$: factorial (as in $n!$), $a$: complex variable, $t_j$: eigenvalues of $𝐓$ , $b$: complex variable, $c$: complex variable and $k$: nonnegative integer

Referenced by:

Erratum (V1.0.25) for Equation (35.7.3)

Permalink:

http://dlmf.nist.gov/35.7.E3

Encodings:

pMML, png, TeX

Notational change (effective with 1.0.25):

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.

See also:

Annotations for §35.7(ii), §35.7(ii), §35.7 and Ch.35

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13: Bibliography M

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Notes:

MPFR is a C library for multiple-precision floating-point computations with correct rounding. The main goal of MPFR is to provide a library for multiple-precision floating-point computation which is both efficient and has well-defined semantics. MPFR includes most of the elementary functions. It also implements the gamma function, and more special functions are planned in the future.

External Links:

MPFR

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX

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14: 10.21 Zeros

… ►For the first zeros rounded numerical values of the coefficients are given by …

15: Errata

… ►

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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