sin %253F %253C%253D %253F
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1: 19.2 Definitions
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►Assume and , except that one of them may be 0, and .
…The integral for is well defined if , and the Cauchy principal value (§1.4(v)) of is taken if vanishes at an interior point of the integration path.
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►If , then is pure imaginary.
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§19.2(iv) A Related Function:
… ►For the special cases of and see (19.6.15). …2: Bibliography S
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Norm inequalities for a certain class of functions.
Israel J. Math. 10, pp. 364–372.
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Numerical evaluation of integrals of the form and the tabulation of the function
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Quart. J. Mech. Appl. Math. 3 (1), pp. 107–112.
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FGH, a code for the calculation of Coulomb radial wave functions from series expansions.
Comput. Phys. Comm. 146 (2), pp. 250–253.
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On an identity of Ramanujan based on the hypergeometric series
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J. Number Theory 69 (2), pp. 125–134.
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Chebyshev approximation of in
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Math. Comp. 36 (153), pp. 249–253.
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3: 10.34 Analytic Continuation
4: 4.42 Solution of Triangles
5: 19.11 Addition Theorems
6: 19.23 Integral Representations
7: 25.5 Integral Representations
8: 19.5 Maclaurin and Related Expansions
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►where is the Gauss hypergeometric function (§§15.1 and 15.2(i)).
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19.5.4_1
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19.5.4_2
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►where is an Appell function (§16.13).
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►Series expansions of and are surveyed and improved in Van de Vel (1969), and the case of is summarized in Gautschi (1975, §1.3.2).
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9: 1.6 Vectors and Vector-Valued Functions
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►The divergence of a differentiable vector-valued function is
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►The curl of is
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►Sufficient conditions for this result to hold are that and are continuously differentiable on , and is piecewise differentiable.
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►For a sphere , , ,
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►For a vector-valued function ,
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