Wild Guess

Tune: original

A song about the properties of the Euler-Mascheroni constant

If you sum one over k,
And you just won’t stop at all
It will not stop on its way,
Though it rises at a crawl
If you subtract a log, base e
At each step along your path
It converges you will see
Take time to do the math!

Gamma is the limit’s name
It’s easy to approximate
But you cannot hope to claim
We know something of its fate
Our math is still not quite enough
To know its properties, you see
But here’s a guideline that is rough
And I hope you will agree

[Chorus]
You should know the odds if you have to bet
And the odds are a zero to one
So I’m gonna say no, though I’m gonna sweat
For a shred of a proof I have none

Can we find two numbers whole
Their division to be this
If this is to be your goal
Your hope and prays I will dismiss
Rationality is rare
It is much too much to hope
And though I did not say its fair
I am going to say “nope”

[Chorus]

If it’s irrational, you see
Still polynomials abound
Whose co-efficients are in Z
Perhaps one of them can be found
Such that one among its roots
Is this Gamma that we seek
My guess it will bear little fruits
Though my arguments are weak

[Chorus]

Algebraic over pi
Or algebraic over e
Oh, tell me, why you try
Why you cannot let this be
It’s so easy just to guess
To just give up and say “no”
We are not assured success
Though the odds are good, you know

[Chorus]

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