spf {PWEALL}

A utility function

Description

A utility function to calculate a ratio.

Usage

spf(x=seq(-1,1,by=0.2),eps=1.0e-3)

Arguments

x

A vector

eps

tolerance

Details

This is to calculate

\Phi_l(x)=\frac{\int_0^x s^le^{-s}ds}{x^{l+1}},\hspace{0.5cm}l=0,1,2.

This function is well defined even when x=0. However, it is numerical chanllenging to calculate it when x is small. So when |x|\le \code{eps} we approximate this function and the absolute error is \code{eps}^5.

Value

fx1

when l=0;

fx2

when l=1;

fx3

when l=2.

Note

Version 1.0 (7/19/2016)

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

Examples

fun<-spf(x=seq(-1,1,by=0.2),eps=1.0e-3)
fun