# analytic evaluation of $\int_{0}^{\infty} \frac{dx}{\mathrm{Bi}(x)}$

So, just out of random curiosity, I'm trying to find an analytic expression for the following definite integral:

$$\int_{0}^{\infty} \frac{dx}{\mathrm{Bi}(x)}$$.

Where $\mathrm{Bi}(x)$ is the Airy Bi function. Wolfram alpha gives a very messy series for $\frac{1}{\mathrm{Bi}(x)}$, and I couldn't find the numerical evaluation of it in either Plouffe's inverter or the Inverse Symbolic Calculator. evaluation by mpmath below:

>>> quad(lambda x: 1/airybi(x), [0,inf])
mpf('1.9365573326233994')

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How about calling it deoxygerbe's constant? – Fabian May 12 '12 at 4:33