gives the confluent Heun function.
- HeunC belongs to the Heun class of functions and occurs in quantum mechanics, mathematical physics and applications.
- Mathematical function, suitable for both symbolic and numerical manipulation.
- HeunC[q,α,γ,δ,ϵ,z] satisfies the confluent Heun differential equation .
- The HeunC function is the regular solution of the confluent Heun equation that satisfies the condition HeunC[q,α,γ,δ,ϵ,0]=1.
- HeunC has a branch cut discontinuity in the complex plane running from to .
- For certain special arguments, HeunC automatically evaluates to exact values.
- HeunC can be evaluated for arbitrary complex parameters.
- HeunC can be evaluated to arbitrary numerical precision.
- HeunC automatically threads over lists.
Examplesopen allclose all
Numerical Evaluation (8)
The precision of the output tracks the precision of the input:
HeunC can take one or more complex number parameters:
HeunC can take complex number arguments:
Finally, HeunC can take all complex number input:
Evaluate HeunC efficiently at high precision:
Evaluate HeunC for points at branch cut to :
Specific Values (3)
Function Properties (1)
HeunC can be simplified to Hypergeometric1F1 function in the following case:
The -derivative of HeunC is HeunCPrime:
Higher derivatives of HeunC are calculated using HeunCPrime:
Solve the confluent Heun differential equation using DSolve:
Solve the initial value problem for the confluent Heun differential equation:
Plot the solution for different values of the accessory parameter q:
Directly solve the confluent Heun differential equation:
HeunC with specific parameters solves the Mathieu equation:
Construct the general solution of the Mathieu equation in terms of HeunC functions:
Properties & Relations (3)
HeunC is analytic at the origin:
is a singular point of the HeunC function:
Except for this singular point, HeunC can be calculated at any finite complex :
The derivative of HeunC is HeunCPrime:
Possible Issues (1)
HeunC cannot be evaluated if is a nonpositive integer (so-called logarithmic cases):
Wolfram Research (2020), HeunC, Wolfram Language function, https://reference.wolfram.com/language/ref/HeunC.html.
Wolfram Language. 2020. "HeunC." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HeunC.html.
Wolfram Language. (2020). HeunC. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HeunC.html