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# Ber

The function is defined through the equation

 (1)

where is a Bessel function of the first kind, so

 (2)

where is the real part.

The function is implemented in the Wolfram Language as KelvinBer[nu, z].

The function has the series expansion

 (3)

where is the gamma function (Abramowitz and Stegun 1972, p. 379), which can be written in closed form as

 (4)

The special case , commonly denoted , corresponds to

 (5)

where is the zeroth order Bessel function of the first kind. The function has the series expansion

 (6)

which can be written in closed form as

 (7) (8)

Bei, Bessel Function, Kei, Kelvin Functions, Ker

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## References

Abramowitz, M. and Stegun, I. A. (Eds.). "Kelvin Functions." §9.9 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 379-381, 1972.Prudnikov, A. P.; Marichev, O. I.; and Brychkov, Yu. A. "The Kelvin Functions , , and ." §1.7 in Integrals and Series, Vol. 3: More Special Functions. Newark, NJ: Gordon and Breach, pp. 29-30, 1990.Spanier, J. and Oldham, K. B. "The Kelvin Functions." Ch. 55 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 543-554, 1987.

Ber

## Cite this as:

Weisstein, Eric W. "Ber." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Ber.html