How do I format the output to include the function definition?

Question

To explain, I do most of my probability homework in Mathematica, and use the typesetting built into Mathematica to finish answers. Often, I want to output a function as the answer to a problem, but I want it to be explicit, that is, in the example below, I create a function, X[x,y,z], and I want the result to not just display the (in this case) piecewise function, but I want it to define it as a function. As an example:

Clear[X, x, y, z]
X[x_, y_, z_] := Piecewise[{{3/(4*Pi), Sqrt[x^2 + y^2 + z^2] <= 1}}, 0]
X[x, y, z]//TraditionalForm

The output of this is $$ \left\{ \begin{array}{cc} \frac{3}{4 \pi } & \sqrt{x^2+y^2+z^2}\leq 1 \\ 0 & \text{True} \\ \end{array} \right. $$

I want it (the output) to look (something) like

$$ X(x,y,z)=\left\{ \begin{array}{cc} \frac{3}{4 \pi } & \sqrt{x^2+y^2+z^2}\leq 1 \\ 0 & \text{True} \\ \end{array} \right. $$

Answer 1

To expand my comment into an answer:

HoldForm[X[x, y, z]] == X[x, y, z] // TraditionalForm

$$X(x,y,z)=\left( \left\{ \begin{array}{cc} \frac{3}{4 \pi } & \sqrt{x^2+y^2+z^2}\leq 1 \\ 0 & \text{True} \\ \end{array} \right. \right)$$

But Mathematica decides it needs parentheses. I agree that this doesn't look ideal. There are a couple of ways around it. One is that you can manually edit the traditional form in Mathematica. Another option is to piece it together ourselves in a Row (with a goofy equals to nothing):

Clear[traditionalise];
Attributes[traditionalise] = {HoldAll};
traditionalise[f_] := TraditionalForm@Row@{HoldForm@f == " ", f}

traditionalise[X[x,y,z]]

$$ X(x,y,z)=\left\{ \begin{array}{cc} \frac{3}{4 \pi } & \sqrt{x^2+y^2+z^2}\leq 1 \\ 0 & \text{True} \\ \end{array} \right. $$