Question

Why does Wolfram Alpha call the Pochhammer symbol "unfortunate"?

Answer 1

It's explained in the subsequent paragraph.

Answer 2

because putting brackets around something, and sub/superscripts already mean a million other unrelated things.

Answer 3

The notation is pretty easily confused with normal exponential notation. So it becomes a source of confusion or ambiguity. The choice of that particular form of notation is therefore unfortunate.

Answer 4

I personally find this awful:

     5³    =  5 · 5 · 5            Exponentiation
    (5³)   =  5 · 5 · 5            also Exponentiation
     5⁽³⁾  =  5 · 6 · 7            Rising Factorial / Pochhammer
    (5)₃   =  5 · 4 · 3            Falling Factorial

Either I'm wrong or the Wolfram page looks erroneous - they use the **subscript** for Pochhammer even though it's supposed to be the **superscript**

Answer 5

I’ve never heard of this symbol, but based on those two paragraphs, they seem to indicate that (x)_n can be both a rising or falling factorial.

Unless I’m misreading something.

Answer 6

Another problem is that it is ambiguous as to whether it denotes a rising or a *falling* factorial.