hypergeo (version 1.2-13)

is.nonpos: 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, $1/2 +/- sqrt(3)i/2$. These points have unit modulus as do their six transforms by thingfun()
• Function lpham() returns the log of the Pochhammer function $log(Gamma(x+n)/Gamma(x))$

Examples

is.near_integer(-3)

is.zero(4)