sine integrals
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11—20 of 174 matching pages
11: 6.3 Graphics
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12: 7.4 Symmetry
13: 6.4 Analytic Continuation
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6.4.6
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6.4.7
►Unless indicated otherwise, in the rest of this chapter and elsewhere in the DLMF the functions , , , , and assume their principal values, that is, the branches that are real on the positive real axis and two-valued on the negative real axis.
14: 6.13 Zeros
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6.13.1
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and each have an infinite number of positive real zeros, which are denoted by , , respectively, arranged in ascending order of absolute value for .
Values of and to 30D are given by MacLeod (1996b).
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6.13.2
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15: 6.18 Methods of Computation
§6.18 Methods of Computation
… ►Power series, asymptotic expansions, and quadrature can also be used to compute the functions and . …Then , , and … ►§6.18(iii) Zeros
►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. …16: 7.5 Interrelations
17: 8.1 Special Notation
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►Unless otherwise indicated, primes denote derivatives with respect to the argument.
►The functions treated in this chapter are the incomplete gamma functions , , , , and ; the incomplete beta functions and ; the generalized exponential integral
; the generalized sine and cosine integrals
, , , and .
►Alternative notations include: Prym’s functions
, , Nielsen (1906a, pp. 25–26), Batchelder (1967, p. 63); , , Dingle (1973); , , Magnus et al. (1966); , , Luke (1975).
18: 7.2 Definitions
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7.2.8
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, , and are entire functions of , as are and in the next subsection.
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7.2.10
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7.2.11
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