hypergeo (version 1.2-9)

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

• Functionis.near_integer(i)returnsTRUEifiisnear[that is, withintol] an integer; if the option is unset then1e-11is used.
• Functionis.nonpos()returnsTRUEifiis near a nonpositive integer
• Functionis.zero()returnsTRUEifiis, er, near zero
• Functionisgood()checks for all elements ofxhaving absolute values less thantol
• Functionthingfun()transforms input vectorzby 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
• Functioncrit()returns the two critical points,$\frac{1}{2}\pm\frac{\sqrt{3}i}{2}$. These points have unit modulus as do their six transforms bythingfun()
• Functionlpham()returns the log of the Pochhammer function$log\left(\Gamma(x+n)/\Gamma(x)\right)$

Examples

is.near_integer(-3)

is.zero(4)