Jacobi’s
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1: 22.16 Related Functions
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§22.16(ii) Jacobi’s Epsilon Function
►Integral Representations
… ►§22.16(iii) Jacobi’s Zeta Function
… ► ►2: 22.21 Tables
§22.21 Tables
… ► …3: 20.4 Values at = 0
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Jacobi’s Identity
…4: 20.1 Special Notation
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►Jacobi’s original notation: , , , , respectively, for , , , , where .
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►Neville’s notation: , , , , respectively, for , , , , where again .
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►McKean and Moll’s notation: , .
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5: 27.13 Functions
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27.13.5
►One of Jacobi’s identities implies that
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►Also, Milne (1996, 2002) announce new infinite families of explicit formulas extending Jacobi’s identities.
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6: 22.6 Elementary Identities
7: 25.1 Special Notation
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►The main related functions are the Hurwitz zeta function , the dilogarithm , the polylogarithm (also known as Jonquière’s function ), Lerch’s transcendent , and the Dirichlet -functions .
8: 22.1 Special Notation
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►The functions treated in this chapter are the three principal Jacobian elliptic functions , , ; the nine subsidiary Jacobian elliptic functions , , , , , , , , ; the amplitude function ; Jacobi’s epsilon and zeta functions and .
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►Other notations for are and with ; see Abramowitz and Stegun (1964) and Walker (1996).
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9: 20.9 Relations to Other Functions
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►The relations (20.9.1) and (20.9.2) between and (or ) are solutions of Jacobi’s inversion problem; see Baker (1995) and Whittaker and Watson (1927, pp. 480–485).
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