User:Richard Pinch/sandbox-15

Hopf constant

A constant $q_\infty$ associated with the Milne problem in radiative transfer theory. It may be defined as $$ q_\infty = \frac{1}{\pi} \int_0^{\pi/2} \left({\frac{3}{\sin^2\theta} - \frac{1}{1-\theta\cot\theta}} \right) d\theta \ . $$ Its numerical value is $$ q_\infty = 0.7104460895 \dots\ . $$

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press (2003) ISBN 0-521-81805-2 Zbl 1054.00001