of the first and second kinds
(0.012 seconds)
1—10 of 205 matching pages
1: 10.26 Graphics
2: 10.45 Functions of Imaginary Order
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10.45.3
►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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3: 10.34 Analytic Continuation
4: 26.8 Set Partitions: Stirling Numbers
5: 19.4 Derivatives and Differential Equations
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19.4.3
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►If , then these two equations become hypergeometric differential equations (15.10.1) for and .
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6: 10.28 Wronskians and Cross-Products
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10.28.2
7: 26.21 Tables
§26.21 Tables
►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 second kinds, and , for up to 25 and up to ; tabulates partitions and partitions into distinct parts for up to 500. … ►It also contains a table of Gaussian polynomials up to . …8: 10.42 Zeros
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►Properties of the zeros of and may be deduced from those of and , respectively, by application of the transformations (10.27.6) and (10.27.8).
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