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Development of the Hubbell Rectangular Source Integral

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Abstract

The integral

$$\int_0^b {\frac{1}{{\sqrt {x^2 + 1} }}\tan ^{ - 1} } \left[ {\frac{a}{{\sqrt {x^2 + 1} }}} \right]{\text{d}}x$$

is the leading term in a series solution appearing in the computation of the radiation field from a plane isotropic rectangular source, and is known as the ‘Hubbell Rectangular Source Integral’ – HRSI. A survey of various properties of HRSI, namely its series representations, asymptotic formulas, recurrence relations and approximation formulas, as well as some previous generalizations is presented here. In addition, a further generalization of HRSI using a modified form of the Gauss hypergeometric function is proposed.

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Authors and Affiliations

  1. Department of Mathematics & Computer Science, Kuwait University, PO Box 5969, Safat, 13060, Kuwait

    S. L. Kalla, A. H. Al-Shammery & H. G. Khajah

Authors
  1. S. L. Kalla
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  2. A. H. Al-Shammery
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  3. H. G. Khajah
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Kalla, S.L., Al-Shammery, A.H. & Khajah, H.G. Development of the Hubbell Rectangular Source Integral. Acta Applicandae Mathematicae 74, 35–55 (2002). https://doi.org/10.1023/A:1020525315841

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