Expint function

exponential functions

Expint functions as per the Gnu Scientific Library, reference manual section 7.17 and AMS-55, chapter 5. These functions are declared in header file gsl_sf_expint.h.

expint_E1(x, give=FALSE, strict=TRUE)
expint_E2(x, give=FALSE, strict=TRUE)
expint_En(n, x, give=FALSE, strict=TRUE)
expint_Ei(x, give=FALSE, strict=TRUE)
Shi(x, give=FALSE, strict=TRUE)
Chi(x, give=FALSE, strict=TRUE)
expint_3(x, give=FALSE, strict=TRUE)
Si(x, give=FALSE, strict=TRUE)
Ci(x, give=FALSE, strict=TRUE)
atanint(x, give=FALSE, strict=TRUE)

Arguments

• x: input: real values

• n: input: integer values

• give: Boolean with TRUE meaning to return a list of three items: the value, an estimate of the error, and a status number

• strict: Boolean, with TRUE meaning to return NaN

  if status is an error

Note

Function expint_En() requires GSL version 1.8 or later.

References

https://www.gnu.org/software/gsl/

Author(s)

Robin K. S. Hankin

Examples

x <- seq(from=0.5, to=1, by=0.01)
cbind(x,Si(x),Ci(x),expint_Ei(x),expint_E1(x))  #table 5.1 of AS, p239

x <- seq(from=0, to=12, len=100)
plot(x,Ci(x),col="black",type="l",xaxt="n",yaxt="n",bty="n",
         xlab="",ylab="",main="Figure 5.6, p232",
         xlim=c(0,12),ylim=c(-1,2.0))
lines(x,Si(x))
axis(1,pos=0)
axis(2,pos=0)
 abline(h=pi/2,lty=2)

# Table 5.4, page 245:
 xvec <- seq(from=0,by=0.01,len=20)
 nvec <- c(2,3,4,10,20)
 x <- kronecker(xvec,t(rep(1,5)))
 n <- kronecker(t(nvec),rep(1,20))
 ans <- cbind(x=xvec,expint_En(n,x))
 rownames(ans) <- rep(" ",length(xvec))
 colnames(ans) <- c("x",paste("n=",nvec,sep=""))
 class(ans) <- "I do not understand the first column"

 ans