►and , are real and linearly independent solutions of (10.45.1):
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►In consequence of (10.45.5)–(10.45.7), and comprise a numerically satisfactory pair of solutions of (10.45.1) when is large, and either and , or and , comprise a numerically satisfactory pair when is small, depending whether or .
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►For graphs of and see §10.26(iii).
►For properties of and , including uniform asymptotic expansions for large and zeros, see Dunster (1990a).
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►Abramowitz and Stegun (1964, Chapter 24) tabulates binomial coefficients for up to 50 and up to 25; extends Table 26.4.1 to ; tabulates Stirling numbers of the first and secondkinds, and , for up to 25 and up to ; tabulates partitions and partitions into distinct parts for up to 500.
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►It also contains a table of Gaussian polynomials up to .
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►If
is fixed, then throughout the interval , is positive and increasing, and is positive and decreasing.
►If
is fixed, then throughout the interval , is decreasing, and is increasing.
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