The integrability of generalized Garrett-Stanojević sums
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- by Niranjan Singh and K. M. Sharma PDF
- Proc. Amer. Math. Soc. 104 (1988), 135-144 Request permission
Abstract:
In this paper we have defined the generalized Garrett-Stanojević cosine sums \[ {h_n}\left ( x \right ) = \sum \limits _{p = 0}^n {S_p^{r - 1}{\Delta ^r}{a_p}} \] and have proved that under suitable conditions ${h_n} \to h$ in the ${L^1}$-norm, where $h\left ( x \right ) = {a_0}/2 + \sum \nolimits _{n = 1}^\infty {{a_n}\cos nx}$. If $r = 1$, then ${h_n}\left ( x \right )$ reduces to the modified cosine sums introduced by Rees and Stanojević.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 135-144
- MSC: Primary 42A20; Secondary 42A24
- DOI: https://doi.org/10.1090/S0002-9939-1988-0929424-5
- MathSciNet review: 929424