sine integrals
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21—30 of 174 matching pages
21: 6.12 Asymptotic Expansions
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►For the function see §9.7(i).
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►The asymptotic expansions of and are given by (6.2.19), (6.2.20), together with
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6.12.3
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6.12.4
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6.12.5
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22: 6.17 Physical Applications
§6.17 Physical Applications
… ►Lebedev (1965) gives an application to electromagnetic theory (radiation of a linear half-wave oscillator), in which sine and cosine integrals are used.23: 7.1 Special Notation
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►The main functions treated in this chapter are the error function ; the complementary error functions and ; Dawson’s integral
; the Fresnel integrals
, , and ; the Goodwin–Staton integral
; the repeated integrals of the complementary error function ; the Voigt functions and .
►Alternative notations are , , , , , , , .
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24: 7.3 Graphics
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25: 7.20 Mathematical Applications
26: 6.16 Mathematical Applications
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§6.16(i) The Gibbs Phenomenon
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6.16.2
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6.16.3
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►Hence, if is fixed and , then , , or according as , , or ; compare (6.2.14).
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►The first maximum of for positive occurs at and equals ; compare Figure 6.3.2.
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27: 6.6 Power Series
28: 10.15 Derivatives with Respect to Order
29: 7.23 Tables
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Abramowitz and Stegun (1964, Chapter 7) includes , , , 10D; , , 8S; , , 7D; , , , 6S; , , 10D; , , 9D; , , , 7D; , , , , 15D.
Zhang and Jin (1996, pp. 637, 639) includes , , , 8D; , , , 8D.
Zhang and Jin (1996, p. 642) includes the first 10 zeros of , 9D; the first 25 distinct zeros of and , 8S.