si
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11—20 of 25 matching pages
11: Guide to Searching the DLMF
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Table 2: Wildcard Examples
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►DLMF search is generally case-insensitive except when it is important to be case-sensitive, as when two different special functions have the same standard names but one name has a lower-case initial and the other is has an upper-case initial, such as si and Si, gamma and Gamma.
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Query | What it stands for |
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si$ |
si, sin, sine, sinh, sinc, sinInt, similar, … |
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The following standard special functions: si, Si, ci, Ci, shi, Shi, ce, Ce, se, Se, ln, Ln, Lommels, LommelS, Jacobiphi, and the list is still growing.
12: 6.5 Further Interrelations
13: 6.20 Approximations
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Luke and Wimp (1963) covers for (20D), and and for (20D).
Luke (1969b, pp. 41–42) gives Chebyshev expansions of , , and for , . The coefficients are given in terms of series of Bessel functions.
Luke (1969b, pp. 402, 410, and 415–421) gives main diagonal Padé approximations for , , (valid near the origin), and (valid for large ); approximate errors are given for a selection of -values.
14: 10.15 Derivatives with Respect to Order
15: 6.6 Power Series
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6.6.5
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16: 6.16 Mathematical Applications
17: 6.10 Other Series Expansions
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6.10.4
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18: 6.18 Methods of Computation
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►Zeros of and can be computed to high precision by Newton’s rule (§3.8(ii)), using values supplied by the asymptotic expansion (6.13.2) as initial approximations.
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19: 10.60 Sums
20: 6.7 Integral Representations
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6.7.9
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