ComplexInfinity

ComplexInfinity

represents a quantity with infinite magnitude, but undetermined complex phase.

Details

Examples

open allclose all

Basic Examples  (1)

Division by 0:

Scope  (4)

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:

Applications  (2)

Set up a seemingly "analytic" function that is infinite in the whole left halfplane:

Plotting shows details of the numerical calculation:

Asymptotics of the LogGamma function at ComplexInfinity:

Properties & Relations  (6)

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:

Possible Issues  (4)

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:

Neat Examples  (2)

Infinite arguments of undetermined phase in all elementary functions:

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

Wolfram Research (1988), ComplexInfinity, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexInfinity.html.

Text

Wolfram Research (1988), ComplexInfinity, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexInfinity.html.

BibTeX

@misc{reference.wolfram_2021_complexinfinity, author="Wolfram Research", title="{ComplexInfinity}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexInfinity.html}", note=[Accessed: 18-May-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_complexinfinity, organization={Wolfram Research}, title={ComplexInfinity}, year={1988}, url={https://reference.wolfram.com/language/ref/ComplexInfinity.html}, note=[Accessed: 18-May-2021 ]}

CMS

Wolfram Language. 1988. "ComplexInfinity." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComplexInfinity.html.

APA

Wolfram Language. (1988). ComplexInfinity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComplexInfinity.html