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Date: 18-8-2019
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Date: 23-8-2018
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Date: 19-5-2018
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By analogy with the lemniscate functions, hyperbolic lemniscate functions can also be defined
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(1) |
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(2) |
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(3) |
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(4) |
where is a hypergeometric function.
Let and
, and write
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(5) |
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(6) |
where is the constant obtained by setting
and
, which is given by
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(7) |
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(8) |
with is a complete elliptic integral of the first kind. Ramanujan showed that
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(9) |
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(10) |
and
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(11) |
(Berndt 1994).
REFERENCES:
Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 255-258, 1994.
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