is.nonpos {hypergeo}

Various utilities

Description

Various utilities needing nonce functions

Usage

is.near_integer(i, tol=getOption("tolerance"))
is.nonpos(i)
is.zero(i)
isgood(x, tol)
thingfun(z, complex=FALSE)
crit(...)
lpham(x,n)

Arguments

i

Numerical vector of suspected integers

tol

Tolerance

x

Argument to isgood() and lpham()

z

Complex vector

complex

In function thingfun(), Boolean with default FALSE meaning to return the modulus of the transforms and TRUE meaning to return the complex values themselves

n

second argument to lpham()

...

Ignored

Details

• Function is.near_integer(i) returns TRUE if i is “near” [that is, within tol] an integer; if the option is unset then 1e-11 is used.

• Function is.nonpos() returns TRUE if i is near a nonpositive integer

• Function is.zero() returns TRUE if i is, er, near zero

• Function isgood() checks for all elements of x having absolute values less than tol

• Function thingfun() transforms input vector z by each of the six members of the anharmonic group, viewed as a subgroup of the Mobius group of functions. It returns a real six-column matrix with columns being the modulus of z,z/(z-1),1-z,1/z,1/(1-z),1-1/z. These six columns correspond to the primary argument in equations 15.3.3 to 15.3.9, p551 of AMS-55

• Function crit() returns the two critical points, \frac{1}{2}\pm\frac{\sqrt{3}i}{2}. These points have unit modulus as do their six transforms by thingfun()

• Function lpham() returns the log of the Pochhammer function log\left(\Gamma(x+n)/\Gamma(x)\right)

Note

Function isgood() uses zero as the default tolerance (argument tol passed in from hypergeo()); compare the different meaning of tol used in is.near_integer().

Here, “integer” means one of the sequence 0,\pm 1,\pm 2,\ldots [ie not the Gaussian integers].

Author(s)

Robin K. S. Hankin

Examples

is.near_integer(-3)

is.zero(4)