" wrote:

Previously you wrote:
TDist(x,df,2) = BetaDist(df/(df+x²), df/2, 0.5)

What would be the BetaDist() equivalent for TDist(x,df,1)?
Or doesn't the question make sense to ask?

The t distribution is symmetric about zero, so
TDist(x,df,1) = TDist(x,df,2)/2 €¦

Based on the wikipedia plots and my vague recollection of
the t-distribution plots, shouldn't alpha (df/2) be less than
beta (0.5) in order to get a curve similar to the t-distribution?

Again, the easiest way to verify the relationship between cumulative beta
and t distributions is to calculate both formulas for various {x,df} pairs
where df is an integer.

The first Wikipedia beta distribution formula implies that
f(x,a,b) = f(1-x,b,a)

Excels BetaDist function has no cumulative=false option, but you can
calculate the beta pdf directly from that Wikipedia formula as
= EXP(GAMMALN(a+b)-GAMMALN(a)-GAMMALN(b))*x^(a-1)*(1-x)^(b-1)
= EXP(GAMMALN(a+b)-GAMMALN(a)-GAMMALN(b)+LN(x)*(a-1)+LN(1-x)*(b-1))

Note that this beta pdf is not the t pdf. By the chain rule
http://mathworld.wolfram.com/ChainRule.html
you would multiply the Beta pdf corresponding to TDist(x,df,2) by
ABS(df)/(df+x^2)^2
To get the t pdf.

Jerry