Jacobi amplitude function
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1: 22.16 Related Functions
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§22.16(i) Jacobi’s Amplitude () Function
►Definition
… ►Quasi-Periodicity
… ►Integral Representation
… ► …2: 22.21 Tables
§22.21 Tables
…3: 22.19 Physical Applications
4: 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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5: 22.20 Methods of Computation
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§22.20(vi) Related Functions
…6: 22.14 Integrals
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22.14.3
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7: 19.25 Relations to Other Functions
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19.25.30
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8: 29.2 Differential Equations
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29.2.5
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9: Errata
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Equation (22.19.3)
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22.19.3
Originally the first argument to the function was given incorrectly as . The correct argument is .
Reported 2014-03-05 by Svante Janson.
10: 29.1 Special Notation
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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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