relation to sine and cosine integrals
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11—20 of 52 matching pages
11: 14.5 Special Values
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§14.5(v) ,
►In this subsection and denote the complete elliptic integrals of the first and second kinds; see §19.2(ii). … ►
14.5.21
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§14.5(vi) Addendum to §14.5(ii): ,
…12: 28.10 Integral Equations
§28.10 Integral Equations
►§28.10(i) Equations with Elementary Kernels
… ►§28.10(ii) Equations with Bessel-Function Kernels
… ►§28.10(iii) Further Equations
… ►For relations with variable boundaries see Volkmer (1983).13: 19.6 Special Cases
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19.6.8
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14: Bibliography S
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A method of generating integral relations by the simultaneous separability of generalized Schrödinger equations.
SIAM J. Math. Anal. 10 (4), pp. 823–838.
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Complements to asymptotic development of sine cosine integrals, and auxiliary functions.
Univ. Beograd. Publ. Elecktrotehn. Fak., Ser. Mat. Fiz. 461–497, pp. 185–191.
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Integral equations and relations for Lamé functions and ellipsoidal wave functions.
Proc. Cambridge Philos. Soc. 64, pp. 113–126.
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Algorithm 911: multiple-precision exponential integral and related functions.
ACM Trans. Math. Software 37 (4), pp. Art. 46, 16.
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Automatic computing methods for special functions. III. The sine, cosine, exponential integrals, and related functions.
J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 291–311.
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15: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Connection between quantum systems involving the fourth Painlevé transcendent and -step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial.
J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..
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Recursion relations for the - symbols.
Nuclear Physics A 113 (1), pp. 215–220.
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Evaluation of complex logarithms and related functions.
SIAM J. Numer. Anal. 18 (4), pp. 744–750.
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A new symmetry related to
for classical basic hypergeometric series.
Adv. in Math. 57 (1), pp. 71–90.
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16: 1.17 Integral and Series Representations of the Dirac Delta
§1.17 Integral and Series Representations of the Dirac Delta
… ►§1.17(ii) Integral Representations
… ►The inner integral does not converge. … ►Sine and Cosine Functions
… ►Equations (1.17.12_1) through (1.17.16) may re-interpreted as spectral representations of completeness relations, expressed in terms of Dirac delta distributions, as discussed in §1.18(v), and §1.18(vi) Further mathematical underpinnings are referenced in §1.17(iv). …17: 10.9 Integral Representations
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Poisson’s and Related Integrals
… ►Schläfli’s and Related Integrals
… ►Mehler–Sonine and Related Integrals
… ►§10.9(ii) Contour Integrals
… ►See Paris and Kaminski (2001, p. 116) for related results. …18: 19.10 Relations to Other Functions
§19.10 Relations to Other Functions
►§19.10(i) Theta and Elliptic Functions
►For relations of Legendre’s integrals to theta functions, Jacobian functions, and Weierstrass functions, see §§20.9(i), 22.15(ii), and 23.6(iv), respectively. … ►§19.10(ii) Elementary Functions
… ►In each case when , the quantity multiplying supplies the asymptotic behavior of the left-hand side as the left-hand side tends to 0. …19: 19.7 Connection Formulas
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