R: Dirichlet Eta Function

eta {pracma} | R Documentation

## Dirichlet Eta Function

### Description

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

### Usage

    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.

### Note

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

### References

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

### See Also

`gammaz`, `zeta`

### Examples

    z <- 0.5 + (1:5)*1i
    eta(z)
    z <- c(0, 0.5+1i, 1, 1i, 2+2i, -1, -2, -1-1i)
    eta(z)

[Package pracma version 2.0.4 Index]