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11—20 of 40 matching pages
11: Bille C. Carlson
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►This symmetry led to the development of symmetric elliptic integrals, which are free from the transformations of modulus and amplitude that complicate the Legendre theory.
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12: Notices
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Index of Selected Software Within the DLMF Chapters
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Within each of the DLMF chapters themselves we will provide a list of research software for the functions discussed in that chapter. The purpose of these listings is to provide references to the research literature on the engineering of software for special functions. To qualify for listing, the development of the software must have been the subject of a research paper published in the peer-reviewed literature. If such software is available online for free download we will provide a link to the software.
In general, we will not index other software within DLMF chapters unless the software is unique in some way, such as being the only known software for computing a particular function.
13: 31.14 General Fuchsian Equation
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►The three sets of parameters comprise the singularity parameters
, the exponent parameters
, and the
free accessory parameters
.
With and the total number of free parameters is .
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14: Bibliography N
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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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15: 5.20 Physical Applications
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►Suppose the potential energy of a gas of point charges with positions and free to move on the infinite line , is given by
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►For charges free to move on a circular wire of radius ,
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16: About the Project
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►The results have been published in book form as the NIST Handbook of Mathematical Functions, by Cambridge University Press, and disseminated in the free electronic Digital Library of Mathematical Functions.
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17: 16.10 Expansions in Series of Functions
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►Here , , and are free real or complex parameters.
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18: 21.9 Integrable Equations
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►These parameters, including , are not free: they are determined by a compact, connected Riemann surface (Krichever (1976)), or alternatively by an appropriate initial condition (Deconinck and Segur (1998)).
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19: Bibliography F
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Portable Special Function Routines.
In Portability of Numerical Software (Oak Brook, Illinois, 1976), W. R. Cowell (Ed.),
Lecture Notes in Computer Science, Vol. 57, pp. 452–483.
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20: 18.21 Hahn Class: Interrelations
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