NAG Library Function Document

nag_exp_integral (s13aac)

1: x – doubleInput: On entry: the argument $x$ of the function.
Constraint: $x > 0.0$ .
2: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_REAL_ARG_LE: On entry, x must not be less than or equal to 0.0: $x = 〈value〉$ .
The function is not defined for this value and the result returned is zero.

δ

and

ε

are the relative errors in argument and result respectively, then in principle,

|ε| ≃ |(e^{- x} / E_{1} (x)) δ|

, so the relative error in the argument is amplified in the result by at least a factor

e^{- x} / E_{1} (x)

. The equality should hold if

δ

is greater than the machine precision (

δ

due to data errors etc.), but if

δ

is simply a result of round-off in the machine representation, it is possible that an extra figure may be lost in internal calculation and round-off.

It should be noted that, for small

x

, the amplification factor tends to zero and eventually the error in the result will be limited by machine precision.

For large

x

ε \sim x δ = Δ

, the absolute error in the argument.

To guard against producing underflows, if

x

is larger than a machine-dependent value

x_{hi}

, the result is set directly to zero.

None.

The following program reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.