# String Theory Trivia Question

1. May 7, 2005

### rick1138

I am sure that everyone here is familiar with the story of Gabriel Veneziano's initial push into string theory by noticing Euler's beta function in a math book. Does anyone happen to know what the book was?

2. May 7, 2005

Staff Emeritus
Gee, almost any advanced calculus book or table of integrals would have it. The beta function is an important one, just like the gamma function from which it derives.

3. May 7, 2005

### dextercioby

I'm sorry,SA,but it's the other way around,at least the names would indicate that:

$$B(p,q)=:\int_{0}^{1} x^{p-1}(1-x)^{q-1} \ dx \ ,\mbox{Re(p)}>0,\mbox{Re(q)}>0$$

is called Eulerian Integral of the First Kind ("Beta Euler").

$$\Gamma (z)=:\int_{0}^{\infty} e^{-t}t^{z-1} \ dt \ , \mbox{Re(z)}>0$$

is called Eulerian Integral of the Second Kind ("Gamma Euler").

$$\Gamma (z)=\lim_{n\rightarrow +\infty} n^{z}B(z,n+1) \ , \ n\in\mathbb{N}$$

$$B(p,q)=\frac{\Gamma (p)\Gamma (q)}{\Gamma (p+q)} \ , \ \mbox{Re(p)}>0,\mbox{Re(q)}>0$$

To the OP:there's only one way to find out:a(n) (auto)biography of Mr.Veneziano.

Daniel.

Last edited: May 7, 2005
4. May 7, 2005

Staff Emeritus
Your last relation was the one I was thinking of. Gamma is actually better known than Beta, and that formula for B(p,q) is the one I have usually seen in nonspecialist contexts. And I believe it was this form that Veneziano got his idea from too.

5. May 7, 2005

### dextercioby

I guess i'll have to look into Whittaker & Watson.Maybe they give a short history,too.The formulas i posted were from some notes taken a long time ago.

Daniel.

P.S.I knew you meant that formula

6. May 7, 2005

### dextercioby

I strongly reccomend Whittaker E.T. and Wattson G.N. "A course of Modern Analysis",CUP (i have the 4-the edition,1927),for the best account on Euler functions i've ever seen*.

These functions were probably looked upon in a math book (maybe even W & W) by Veneziano,when he tried to clear up for himself all those renormalization calculations in the SM...

Daniel.

P.S.(as an edit) *On page 259 (of the IV-th ed.),as the first reference,the book by N.Nielsen "Handbuch der Theorie der Gamma-Funktion" (Leipzig,1906) is said to give a complete bibliography.

Last edited: May 7, 2005
7. May 10, 2005

### rick1138

This was a trivia question, not a question of the type, "What are the beta and gamma functions?".