Dirichlet Eta Function

Dirichlet's eta function valid in the entire complex plane.

eta(z)

Arguments

z

Real or complex number or a numeric or complex vector.

Details

Computes the eta function for complex arguments using a series expansion.

Accuracy is about 13 significant digits for abs(z)<100, drops off with higher absolute values.

Value

Returns a complex vector of function values.

References

Zhang, Sh., and J. Jin (1996). Computation of Special Functions. Wiley-Interscience, New York.

Note

Copyright (c) 2001 Paul Godfrey for a Matlab version available on Mathwork's Matlab Central under BSD license.

See also

gammaz, zeta

Examples

z <- 0.5 + (1:5)*1i
eta(z)
#> [1] 0.6398619+0.1935145i 0.7595015+0.3816610i 0.9970914+0.5247927i
#> [4] 1.3606677+0.5208038i 1.7467035+0.2246479i
z <- c(0, 0.5+1i, 1, 1i, 2+2i, -1, -2, -1-1i)
eta(z)
#> [1] 0.5000000+0.0000000i 0.6398619+0.1935145i 0.6931472+0.0000000i
#> [4] 0.5325932+0.2293849i 0.9230198+0.1764252i 0.2500000+0.0000000i
#> [7] 0.0000000+0.0000000i 0.2567153-0.2802308i