hypergeometric%20functions
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1: Bibliography D
2: Bibliography C
3: Bibliography K
4: Software Index
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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.
5: Bibliography N
6: 15.10 Hypergeometric Differential Equation
§15.10 Hypergeometric Differential Equation
… βΊSingularity
… βΊSingularity
… βΊSingularity
…7: 20.11 Generalizations and Analogs
§20.11 Generalizations and Analogs
… βΊ … βΊSimilar identities can be constructed for , , and . …For applications to rapidly convergent expansions for see Chudnovsky and Chudnovsky (1988), and for applications in the construction of elliptic-hypergeometric series see Rosengren (2004). βΊ§20.11(iv) Theta Functions with Characteristics
…8: 13.30 Tables
§13.30 Tables
βΊΕ½urina and Osipova (1964) tabulates and for , , , 7D or 7S.
Slater (1960) tabulates for , , and , 7–9S; for and , 7D; the smallest positive -zero of for and , 7D.
Abramowitz and Stegun (1964, Chapter 13) tabulates for , , and , 8S. Also the smallest positive -zero of for and , 7D.
Zhang and Jin (1996, pp. 411–423) tabulates and for , , and , 8S (for ) and 7S (for ).