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Date: 23-12-2018
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Date: 13-6-2018
1159
Date: 13-6-2018
864
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There are at least two integrals called the Poisson integral. The first is also known as Bessel's second integral,
(1) |
where is a Bessel function of the first kind and is a gamma function. It can be derived from Sonine's integral. With , the integral becomes Parseval's integral.
In complex analysis, let be a harmonic function on a neighborhood of the closed disk , then for any point in the open disk ,
(2) |
In polar coordinates on ,
(3) |
where and is the Poisson kernel. For a circle,
(4) |
For a sphere,
(5) |
where
(6) |
REFERENCES:
Krantz, S. G. "The Poisson Integral." §7.3.1 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 92-93, 1999.
Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 373-374, 1953.
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علامات بسيطة في جسدك قد تنذر بمرض "قاتل"
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أول صور ثلاثية الأبعاد للغدة الزعترية البشرية
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مكتبة أمّ البنين النسويّة تصدر العدد 212 من مجلّة رياض الزهراء (عليها السلام)
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