Whittaker%20functions
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1: Bibliography D
2: 20 Theta Functions
Chapter 20 Theta Functions
…3: 23 Weierstrass Elliptic and Modular
Functions
Chapter 23 Weierstrass Elliptic and Modular Functions
…4: 20.7 Identities
§20.7(v) Watson’s Identities
… βΊ§20.7(vi) Landen Transformations
… βΊ§20.7(vii) Derivatives of Ratios of Theta Functions
… βΊSee Lawden (1989, pp. 19–20). …5: 12.19 Tables
§12.19 Tables
… βΊKireyeva and Karpov (1961) includes for , , and , , 7D.
Karpov and Δistova (1964) includes for , ; , , 6D.
Karpov and Δistova (1968) includes and for and = 0(.001 or .0001)5, , 7D or 8S.
Murzewski and Sowa (1972) includes for , , 7S.
6: 5.11 Asymptotic Expansions
7: Software Index
Open Source | With Book | Commercial | |||||||||||||||||||||||
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20 Theta Functions | |||||||||||||||||||||||||
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Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.
8: 2.11 Remainder Terms; Stokes Phenomenon
9: Errata
This equation was updated to include the definition of Bessel polynomials in terms of Laguerre polynomials and the Whittaker confluent hypergeometric function.
Originally the in front of the was given incorrectly as .
Reported 2017-02-02 by Daniel Karlsson.
Originally the left-hand side was given correctly as ; the equation is true also for .