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The Summation of the Integral Conjugate to the Fourier Integral of the Finite Type and Of the Conjugate Series


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1 Ravenshaw College, Cuttack, India
     

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The integral conjugate to the Denjoy-Fourier Integral of the finite type [7] is

∫(bs cos sx-as sin sx)ds,                                               (1)

where

as = 1/π∫f(t) cos st dt, bs = 1/π∫f(t) sin st dt,                  (2)

and f (x) is supposed to be integrable-D in (-π, π) and to be zero outside this interval.


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  • The Summation of the Integral Conjugate to the Fourier Integral of the Finite Type and Of the Conjugate Series

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Authors

Ramanath Mohanty
Ravenshaw College, Cuttack, India

Abstract


The integral conjugate to the Denjoy-Fourier Integral of the finite type [7] is

∫(bs cos sx-as sin sx)ds,                                               (1)

where

as = 1/π∫f(t) cos st dt, bs = 1/π∫f(t) sin st dt,                  (2)

and f (x) is supposed to be integrable-D in (-π, π) and to be zero outside this interval.