“Hyperbolic Lemniscate Function”的概念、定义、习题解题方法及翻译-数学辞典

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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