- Mathematical function, suitable for both symbolic and numerical manipulation.
- For positive real values of parameters, . For other values, is defined by analytic continuation.
- KelvinKei[n,z] has a branch cut discontinuity in the complex z plane running from to .
- KelvinKei[z] is equivalent to KelvinKei[0,z].
- For certain special arguments, KelvinKei automatically evaluates to exact values.
- KelvinKei can be evaluated to arbitrary numerical precision.
- KelvinKei automatically threads over lists.
Examplesopen allclose all
Basic Examples (6)
Series expansion at Infinity:
Numerical Evaluation (4)
Specific Values (3)
Plot the KelvinKei function for integer () and half-integer () orders:
Function Properties (11)
KelvinKei is neither non-decreasing nor non-increasing:
KelvinKei is not injective:
KelvinKei is neither non-negative nor non-positive:
KelvinKei has both singularity and discontinuity for z≤0:
KelvinKei is neither convex nor concave:
Compute the indefinite integral using Integrate:
Series Expansions (5)
Generalizations & Extensions (1)
KelvinKei can be applied to a power series:
Wolfram Research (2007), KelvinKei, Wolfram Language function, https://reference.wolfram.com/language/ref/KelvinKei.html.
Wolfram Language. 2007. "KelvinKei." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/KelvinKei.html.
Wolfram Language. (2007). KelvinKei. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/KelvinKei.html