Derivative of HeunC function

Question

Given the HeunC function: $$ \operatorname{HeunC}\left( \frac{a^2}{2} \sqrt{2k+3},-1/2,-1+\frac{a^2}{2},-\frac{a^2}{8}(-1 +a^2 k), \frac{1}{2}-\frac{a^2}{4}, -\frac{x^2}{a^2} \right) $$ where $a$ is an arbitrary constant and $k$ is an arbitrary positive constant, what is the derivative of this function with respect to $x$?

Answer 1

Here is the derivative of your function with respect to $x$ computed by Maple,

$$\frac{d}{dx} {\it HeunC} \left( A,B,C,D,E,-{\frac {{x}^{2}}{{a}^{2}}} \right) = - \frac{2x}{a^2}{\it HeunCPrime} \left( A,B,C,D,E,-{\frac {{x}^{2}}{{a}^{2}}} \right) $$ where HeunCPrime The derivative of the Heun Confluent function.