The biggest math symbol that I can think of is the Riemann P-symbol

w(z)=P left{ begin{matrix} a & b & c & ; \ alpha & beta & gamma & z \ alpha^prime & beta^prime & gamma^prime & ; end{matrix} right}

The symbol is also known as the Papperitz symbol because Erwin Papperitz invented the symbol for expressing solutions to Bernard Riemann’s differential equation.

Before writing out Riemann’s differential equation, we note that the equation has regular singular points at a, b, and c. In fact, that is its defining feature: it is the most general linear second order differential equation with three regular singular points. The parameters a, b, and c enter the equation in the as roots of an expression in denominators; that’s as it has to be if these are the singular points.

The way the Greek letter parameters enter Riemann’s equation is more complicated, but there is a good reason for the complication: the notation makes solutions transform as simply as possible under a bilinear transformation. This is important because Möbius transformations are the conformal automorphisms of the Riemann sphere.

To be specific, let

m(z) = frac{Az + B}{Cz + D}

be a Möbius transformation. Then

P left{ begin{matrix} a & b & c & ; \ alpha & beta & gamma & z \ alpha^prime & beta^prime & gamma^prime & ; end{matrix} right} = P left{ begin{matrix} m(a) & m(b) & m(c) & ; \ alpha & beta & gamma & m(z) \ alpha^prime & beta^prime & gamma^prime & ; end{matrix} right}

Since the parameters on the top row of the P-symbol are the locations of singularities, when you transform a solution, moving the singularities, the new parameters have to be the new locations of the singularities. And importantly the rest of the parameters do not change.

Now with the motivation aside, we’ll write out Riemann’s differential equation in all its glory.

frac{d^2w}{dz^2} + p(z) frac{dw}{dz} + q(z) frac{w}{(z-a)(z-b)(z-c)} = 0

where

p(z) = frac{1-alpha-alpha^prime}{z-a} + frac{1-beta-beta^prime}{z-b} + frac{1-gamma-gamma^prime}{z-c}

and

q(z) = frac{alphaalpha^prime (a-b)(a-c)} {z-a} +frac{betabeta^prime (b-c)(b-a)} {z-b} +frac{gammagamma^prime (c-a)(c-b)} {z-c}

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