ComplexInfinity

Use ComplexInfinity in numerical functions:

ComplexInfinity absorbs finite real, complex, and symbolic quantities:

Do arithmetic with ComplexInfinity:

Use ComplexInfinity as an expansion point for series:

Set up a seemingly "analytic" function that is infinite in the whole left half-plane:

Plotting shows details of the numerical calculation:

Asymptotics of the LogGamma function at ComplexInfinity:

Use Quiet to suppress messages:

ComplexInfinity can be generated by Simplify and FullSimplify:

ComplexInfinity has indeterminate real and imaginary parts:

ComplexInfinity is not a number:

Obtain ComplexInfinity from limits:

ComplexInfinity behaves like a constant in differentiation:

ComplexInfinity is not a numeric quantity:

ComplexInfinity is a symbol with infinite precision:

ComplexInfinity evaluates to DirectedInfinity:

Use ComplexInfinity with care in boundary conditions of differential equations:

Infinite arguments of undetermined phase in all elementary functions:

Behavior of the exponential function at ComplexInfinity shown on the Riemann sphere: