variation%20of%20real%20or%20complex%20functions
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11—20 of 55 matching pages
11: 23.14 Integrals
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23.14.3
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12: 25.11 Hurwitz Zeta Function
§25.11 Hurwitz Zeta Function
… βΊAs a function of , with () fixed, is analytic in the half-plane . The Riemann zeta function is a special case: … βΊThroughout this subsection . … βΊwhere the integration contour is a loop around the negative real axis as described for (25.5.20). …13: Peter L. Walker
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βΊWalker’s published work has been mainly in real and complex analysis, with excursions into analytic number theory and geometry, the latter in collaboration with Professor Mowaffaq Hajja of the University of Jordan.
βΊWalker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004.
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14: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable.
2nd edition, McGraw-Hill Book Co., New York.
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Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule.
Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.
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A subroutine package for Bessel functions of a complex argument and nonnegative order.
Technical Report
Technical Report SAND85-1018, Sandia National Laboratories, Albuquerque, NM.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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15: 9.18 Tables
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§9.18(ii) Real Variables
… βΊZhang and Jin (1996, p. 337) tabulates , , , for to 8S and for to 9D.
§9.18(iii) Complex Variables
… βΊCorless et al. (1992) gives the real and imaginary parts of for ; 14S.
Gil et al. (2003c) tabulates the only positive zero of , the first 10 negative real zeros of and , and the first 10 complex zeros of , , , and . Precision is 11 or 12S.
16: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Algorithm 912: a module for calculating cylindrical functions of complex order and complex argument.
ACM Trans. Math. Software 37 (4), pp. Art. 47, 25.
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Complex zeros of two incomplete Riemann zeta functions.
Math. Comp. 26 (118), pp. 551–565.
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ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument.
Comput. Phys. Comm. 113 (2-3), pp. 220–238.
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17: 25.12 Polylogarithms
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βΊIn the complex plane has a branch point at .
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βΊFor real or complex
and the polylogarithm
is defined by
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βΊFor each fixed complex
the series defines an analytic function of for .
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…valid when , or , .
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18: Bibliography N
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Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes.
ACM Trans. Math. Software 18 (3), pp. 345–349.
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Complex standard functions and their implementation in the CoStLy library.
ACM Trans. Math. Softw. 33 (1), pp. Article 2.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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19: Foreword
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βΊThe provision of standard reference data of this type is a core function of NIST.
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βΊThe new printed volume, the NIST Handbook of Mathematical Functions, serves a similar function as the original A&S, though it is heavily updated and extended.
The online version, the NIST Digital
Library of Mathematical Functions (DLMF), presents the same technical information along with extensions and innovative interactive features consistent with the new medium.
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βΊThe production of these new resources has been a very complex undertaking some 10 years in the making.
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βΊNovember 20, 2009
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20: 5.22 Tables
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βΊFor early tables for both real and complex variables see Fletcher et al. (1962), Lebedev and Fedorova (1960), and Luke (1975, p. 21).
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