elliptic: eta – R documentation

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eta

Dedekind's eta function

Dedekind's eta function

eta(z, ...)
eta.series(z, maxiter=300)

`z`	Complex argument
`...`	In function `eta()`, extra arguments sent to `theta3()`
`maxiter`	In function `eta.series()`, maximum value of iteration

Function eta() uses Euler's formula, viz

[omitted; see LaTeX version

Function eta.series() is present for validation (and interest) only; it uses the infinite product formula:

[omitted; see LaTeX version]

Robin K. S. Hankin

K. Chandrasekharan 1985. Elliptic functions, Springer-Verlag.

z <- seq(from=1+1i,to=10+0.06i,len=999)
 plot(eta(z))

max(abs(eta(z)-eta.series(z)))

Weierstrass and Jacobi Elliptic Functions

v1.4-0

GPL-2

Authors

Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)

Initial release