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exp function in MATLAB®, see
exp(x) represents the value of the exponential
function at the point x.
The exponential function is defined for all complex arguments.
For most exact arguments, an unevaluated function call is returned subject to some simplifications:
Calls of the form with integer or rational q are rewritten such that q lies in the interval . Explicit results are returned if the denominator of q is 1, 2, 3, 4, 5, 6, 8, 10, or 12.
Further, the following special values are implemented: , , .
A call of the form with
an unevaluated ln(y) and
a constant c (i.e.,
yields the result yc.
The call yields
the result ,
if f is
Floating point results are computed, when the argument is a floating-point number.
Numerical exceptions may happen, when the absolute value of
the real part of a floating-point argument x is
large. If ℜ(x)
< - 7.4 108,
exp(x) may return the truncated result
against underflow). If ℜ(x)
> 7.4 108,
exp(x) may return the floating-point equivalent RD_INF of
infinity. See Example 2.
The protected identifier
E is an alias for
When called with a floating-point argument, the function is
sensitive to the environment variable
DIGITS which determines
the numerical working precision.
We demonstrate some calls with exact and symbolic input data:
exp(1), exp(2), exp(-3), exp(1/4), exp(1 + I), exp(x^2)
Floating point values are computed for floating-point arguments:
exp(1.23), exp(4.5 + 6.7*I), exp(1.0/10^20), exp(123456.7)
Some special symbolic simplifications are implemented:
exp(I*PI), exp(x - 22*PI*I), exp(3 + I*PI)
exp(ln(-2)), exp(ln(x)*PI), exp(lambertW(5))
The truncated result
0.0 may be returned
for floating-point arguments with negative real parts. This prevents
exp(-742261118.6 + 10.0^10*I), exp(-744261118.7 + 10.0^10*I)
limit(x*exp(-x), x = infinity), series(exp(x/(x + 1)), x = 0)
expand(exp(x + y + (sqrt(2) + 5)*PI*I))
exp transforms intervals (of type
exp(-1 ... 1)
Note that the MuPAD® floating-point numbers cannot be arbitrarily large. In the context of floating-point intervals, all values larger than a machine-dependent constant are regarded as “infinite”:
exp(1 ... 1e1000)
Finally, we would like to mention that you can also use
disjunct unions of intervals:
exp((1 ... PI) union (10 ... 20))
Arithmetical expression or a floating-point interval