Symbolic generalized exponential integral (expint) function.
Integral definition:
syms x E1 = expint(x) ⇒ E1 = (sym) E₁(x) rewrite(E1, 'Integral') % doctest: +SKIP ⇒ (sym) ∞ ⌠ ⎮ -t⋅x ⎮ ℯ ⎮ ───── dt ⎮ t ⌡ 1
This can also be written (using the substitution u = t⋅x
) as:
∞ ⌠ ⎮ -u ⎮ ℯ ⎮ ─── du ⎮ u ⌡ x
With two arguments, we have:
E2 = expint(2, x) ⇒ E2 = (sym) E₂(x)
In general:
syms n x En = expint(n, x) ⇒ En = (sym) expint(n, x) rewrite(En, 'Integral') % doctest: +SKIP ⇒ (sym) ∞ ⌠ ⎮ -n -t⋅x ⎮ t ⋅ℯ dt ⌡ 1
Other example:
diff(En, x) ⇒ (sym) -expint(n - 1, x)
See also: expint, @sym/ei.
Package: symbolic