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21—30 of 86 matching pages
21: Bibliography
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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22: 25.12 Polylogarithms
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►The notation was introduced in Lewin (1981) for a function discussed in Euler (1768) and called the dilogarithm in Hill (1828):
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►The notation was used for in Truesdell (1945) for a series treated in Jonquière (1889), hence the alternative name Jonquière’s function.
The special case is the Riemann zeta function: .
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►Further properties include
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23: 10.3 Graphics
§10.3 Graphics
►§10.3(i) Real Order and Variable
… ►§10.3(ii) Real Order, Complex Variable
►In the graphics shown in this subsection, height corresponds to the absolute value of the function and color to the phase. … ►§10.3(iii) Imaginary Order, Real Variable
…24: Bibliography G
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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25: 20 Theta Functions
Chapter 20 Theta Functions
…26: 20.11 Generalizations and Analogs
§20.11 Generalizations and Analogs
… ►It is a discrete analog of theta functions. If both are positive, then allows inversion of its arguments as a modular transformation (compare (23.15.3) and (23.15.4)): … ►Ramanujan’s theta function is defined by … ►§20.11(iv) Theta Functions with Characteristics
…27: Bibliography M
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A dispersion function for plasmas containing superthermal particles.
Physics of Plasmas 2 (6), pp. 2098–2109.
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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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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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28: Bibliography C
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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29: 36.2 Catastrophes and Canonical Integrals
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36.2.28
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