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►The functions treated in this chapter are the three principal Jacobian elliptic functions
, , ; the nine subsidiary Jacobian elliptic functions
, , , , , , , , ; the amplitudefunction
; Jacobi’s epsilon and zeta functions
and .
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►(For other notation see Notation for the Special Functions.)
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►All derivatives are denoted by differentials, not by primes.
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►The notation for the eigenvalues and functions is due to Erdélyi et al. (1955, §15.5.1) and that for the polynomials is due to Arscott (1964b, §9.3.2).
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►where ; see §22.16(i).
The relation to the Lamé functions
, of Ince (1940b) is given by
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