Titlebook: Classical Summability Theory; P.N. Natarajan Book 2017 Springer Nature Singapore Pte Ltd. 2017 Special methods of summability.Silverman-To

大罵

Tractable

Invigorate

逃避現(xiàn)實

觀察

Extramural Grant II: Instrumentation,In the present chapter, more properties of the . method are established. For instance, it is proved that the set . of all . methods is an ordered abelian semigroup and there are infinite chains of . methods from .. A few results on the Cauchy multiplication of certain summable series are also proved.

Fallibility

Michael Rudibaugh Ph.D. CandidateIn this chapter, a new definition of convergence of a double sequence and a double series is introduced and its properties are studied. In the context of this new definition, the Silverman–Toeplitz theorem for four-dimensional infinite matrices is proved. We also prove Schur and Steinhaus theorems for four-dimensional infinite matrices.

compose

Dissertation II: Geo-Techniques,In the context of the new definition of convergence of a double sequence and double series introduced in Chap.?., we define the N?rlund, the Weighted Mean, and the . or Natarajan methods for double sequences and double series and study some of their properties.

漂白

悶熱

Special Summability Methods,In the current chapter, we introduce some special methods of summability, viz. the Abel method, the Weighted Mean method, the Euler method and the . or Natarajan method, and study their properties extensively. The connection between the Abel method and the Natarajan method is brought out.

forbid

More Properties of the , Method and Cauchy Multiplication of Certain Summable Series,In the present chapter, more properties of the . method are established. For instance, it is proved that the set . of all . methods is an ordered abelian semigroup and there are infinite chains of . methods from .. A few results on the Cauchy multiplication of certain summable series are also proved.