Abstract
A representation of a given function f(x) by means of a double integral involving modified Bessel functions of order v is
or also
This is equivalent with the pair of inversion formulas
or
Since for v = ± ½
the equations (3) and (4) become
These are the Laplace transform formulas.
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References
Boas, R. P., 1942: Proc. Nat. Acad. Sci. U.S.A. 28, 21–24.
Boas, R. P., 1942: Bull. Amer. Math. Soc. 48, 286–294.
Meijer, C. S., 1940: Proc. Amsterdam Akad. Wet. 599-608; 702–711.
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Oberhettinger, F. (1972). Integral Transforms with Modified Bessel Functions as Kernel. In: Tables of Bessel Transforms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65462-6_2
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DOI: https://doi.org/10.1007/978-3-642-65462-6_2
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