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11—20 of 882 matching pages
11: 8.26 Tables
§8.26 Tables
… ►§8.26(ii) Incomplete Gamma Functions
… ►§8.26(iii) Incomplete Beta Functions
… ►§8.26(iv) Generalized Exponential Integral
… ►Chiccoli et al. (1988) presents a short table of for , to 14S.
12: 8.5 Confluent Hypergeometric Representations
§8.5 Confluent Hypergeometric Representations
…13: 17.1 Special Notation
14: Bibliography F
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II.
J. Math. Anal. Appl. 7 (3), pp. 440–451.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order.
J. Math. Anal. Appl. 6 (3), pp. 394–403.
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Expansions of hypergeometric functions in hypergeometric functions.
Math. Comp. 15 (76), pp. 390–395.
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Guide to tables of elliptic functions.
Math. Tables and Other Aids to Computation 3 (24), pp. 229–281.
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Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments.
National Physical Laboratory Mathematical Tables, Vol. 4.
Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.
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15: 13.13 Addition and Multiplication Theorems
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►To obtain similar expansions for and , replace in the previous two subsections by .
16: 13.26 Addition and Multiplication Theorems
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►To obtain similar expansions for and , replace in the previous two subsections by .
17: Bibliography S
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Microwave Transmission.
McGraw-Hill Book Co., New York.
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Confluent Hypergeometric Functions.
Cambridge University Press, Cambridge-New York.
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Generalized Hypergeometric Functions.
Cambridge University Press, Cambridge.
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Tables of the integro-exponential functions.
Acta Astronom. 18, pp. 289–311.
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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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18: 8.24 Physical Applications
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►The function appears in: discussions of power-law relaxation times in complex physical systems (Sornette (1998)); logarithmic oscillations in relaxation times for proteins (Metzler et al. (1999)); Gaussian orbitals and exponential (Slater) orbitals in quantum chemistry (Shavitt (1963), Shavitt and Karplus (1965)); population biology and ecological systems (Camacho et al. (2002)).
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19: 28.35 Tables
§28.35 Tables
… ►Zhang and Jin (1996, pp. 521–532) includes the eigenvalues , for , ; (’s) or 19 (’s), . Fourier coefficients for , , . Mathieu functions , , and their first -derivatives for , . Modified Mathieu functions , , and their first -derivatives for , , . Precision is mostly 9S.
§28.35(iii) Zeros
… ►§28.35(iv) Further Tables
►For other tables prior to 1961 see Fletcher et al. (1962, §2.2) and Lebedev and Fedorova (1960, Chapter 11).20: Philip J. Davis
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►He returned to Harvard after the war and completed a Ph.
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►Davis, easing into his role as Chief, did his part to promote the field of numerical analysis at NBS.
He also had a big influence on the development of the NBS Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (A&S), which became one of the most widely distributed and highly cited publications in NIST’s history.
After being asked by Milton Abramowitz to work on the project, he chose to write the Chapter “Gamma Function and Related Functions.
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►Today the DLMF contains close to 600 2D and 3D graphs and more than 200 interactive 3D visualizations.
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