Exponential integral

Exponential integrals.

Procedures:

ei: Exponential integral $\mathrm{Ei}(x)$
e1: Exponential integral $\mathrm{E}_1(x)$ or $\mathrm{E}_1(z)$

Untested procedures:

enz: Exponential integral $\mathrm{E}_n(z)$ , untested for $n \neq 1$

References

Kathleen A. Paciorek. 1970. Algorithm 385: Exponential integral Ei(x). Commun. ACM 13, 7 (July 1970), 446–447. https://doi.org/10.1145/362686.362696
Donald E. Amos. 1990. Algorithms 683: a portable FORTRAN subroutine for exponential integrals of a complex argument. ACM Trans. Math. Softw. 16, 2 (June 1990), 178–182. https://doi.org/10.1145/78928.78934

Uses

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Graph Key

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Used by

Help

Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.
Where possible, edges connecting nodes are given different colours to make them easier to distinguish in large graphs.

Interfaces

public interface e1

Exponential integral $\mathrm{E}_1(x)$ or $\mathrm{E}_1(z)$ .

private function e1x(x)

Exponential integral $\mathrm{E}_1(x)$ .

$\lbrace x \in \mathbb{R} \mid x \neq 0 \rbrace$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	x

Return Value real(kind=wp)

private function e1z(z)

Exponential integral $\mathrm{E}_1(z)$ .

$z \in \mathbb{C} \setminus \left( \lbrace z \in \mathbb{C} \mid \Re(z) \lt 0, \thinspace 0 \lt |\Im(z)| \lt 10^{-6} \rbrace \cup \lbrace 0 \rbrace \right)$

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=wp),	intent(in)			::	z

Return Value complex(kind=wp)

Functions

public function ei(x)

Exponential integral $\mathrm{Ei}(x)$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	x

Return Value real(kind=wp)

public function enz(n, z, show_warning)

Exponential integral $\mathrm{E}_n(z)$ .

Arguments

Type	Intent	Optional		Name
integer(kind=i4),	intent(in)		::	n
complex(kind=wp),	intent(in)		::	z
logical,	intent(in),	optional	::	show_warning	Default=`.true.`

csf_exponential_integral Module

Contents

Interfaces

Functions

Exponential integral

References

Uses

Used by

Interfaces

public interface e1

private function e1x(x)

Arguments

Return Value real(kind=wp)

private function e1z(z)

Arguments

Return Value complex(kind=wp)

Functions

public function ei(x)

Arguments

Return Value real(kind=wp)

public function enz(n, z, show_warning)

Arguments

Return Value complex(kind=wp)