(For other notation see Notation for the Special Functions.)
real variables. |
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complex variable. |
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complementary modulus, . If , then . |
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, |
, (complete elliptic integrals of the first kind (§19.2(ii))). |
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All derivatives are denoted by differentials, not primes.
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 .