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单词 Hyperbolic Lemniscate Function
释义

Hyperbolic Lemniscate Function

By analogy with the Lemniscate Functions, hyperbolic lemniscate functions can also be defined

(1)


(2)

Let and , and write
(3)

where is the constant obtained by setting and . Then
(4)

where is a complete Ramanujan showed
(5)


(6)

and


(7)

(Berndt 1994).

See also Lemniscate Function


References

Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 255-258, 1994.


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