I get a weird exponential inside the function that appears as the result of an integral in Mathematica. Namely, the function
$Hypergeometric1F1^{(1,0,0)}[1, 1, -x^2]$
has the 3-component list in the exponential. I have searched everywhere to find the explanation of the $(1,0,0)$ exponent, but couldn't find it. Does anyone know its meaning?
It seems that number of terms in the exponent must match the number of arguments.
Thanks in advance.
$\operatorname{Hypergeometric1F1}^{(1,0,0)}[1, 1, -x^2]\;$ is the partial derivative of $\;{}_1F_1(x_1;x_2;x_3)\,$ relatively to the first parameter : $\quad\displaystyle\frac{\partial }{\partial x_1}\; {}_1F_1(x_1;x_2;x_3)\;$ taken at $\;x_1=1,\,x_2=1,\,x_3=-x^2$.
$\operatorname{Hypergeometric1F1}^{(0,2,0)}[1, 1, -x^2]\;$ means $\;\;\left.\displaystyle\frac{\partial^2 }{\partial (x_2)^2}\;{}_1F_1(x_1;x_2;x_3)\right|_{x_1=1,\,x_2=1,\,x_3=-x^2}$
and so on...
The same notation is used for other multi-parameters functions.
Wolfram's Derivative operator $D$ is described here with some examples including :
Input : $\quad D[g[x, y], y]$
Output : $\quad g^{(0,1)}[x,y]$