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- W2056516412 abstract "It is shown that if m>0[ frac{x}{(1+x^2)m+1/2}=limε→ +0∫|u|≥εfrac{1}{[1+(x-u)2]m+1/2}km(u)du]holds for all x in the pointwise covergence and if m>½ this equality also holds in the Lp norm convergence (p≥1), where km(x) is a singular integral kernel, that is[ km(x)=(sgn x)2π-2∫∞0e^{-|x|v}frac{dv}{v(J2m(v)+Y2m(v))}.]This equality is an extension of the well-known equality [ frac{x}{1+x2}=limε → +0∫|u|≥εfrac{1}{1+(x-u)2}frac{1}{π u}du.]" @default.
- W2056516412 created "2016-06-24" @default.
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- W2056516412 date "1987-01-01" @default.
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- W2056516412 title "On the Pearson type VII distribution and the singular integral transformation" @default.
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- W2056516412 doi "https://doi.org/10.5036/bfsiu1968.19.7" @default.
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