Watson's Formula
Let 
be a Bessel Function of the First Kind, 
a Bessel Function of the Second Kind, and 
aModified Bessel Function of the First Kind. Also let 
and require 
. Then
The fourth edition of Gradshteyn and Ryzhik (1979), Iyanaga and Kawada (1980), and Ito (1987) erroneously give the exponential with a Plus Sign. A related integral is given by
for
.See also Dixon-Ferrar Formula, Nicholson's Formula
References
Gradshteyn, I. S. and Ryzhik, I. M. Eqns. 6.617.1 and 6.617.2 in Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 710, 1979. Ito, K. (Ed.). Encyclopedic Dictionary of Mathematics, 2nd ed. Cambridge, MA: MIT Press, p. 1806, 1987. Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1476, 1980.
- Extended Cycloid
- Extended Goldbach Conjecture
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- Extended Mean-Value Theorem
- Extended Riemann Hypothesis
- Extension
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- Extensions Calculus
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- Extremal Graph
- Extremals
- Extreme and Mean Ratio
- Extreme Value Distribution
- Extreme Value Theorem