Abstract
We introduce lemniscate-like constants by “twisting” the standard series expansions of the classical lemniscate constants via harmonic-type factors in the summand. Closed-form evaluations for these constants are established, and are then utilized to construct alternate proofs of summation formulae obtained recently via coefficient-extraction techniques applied to Kummer’s classical hypergeometric identity.
(Communicated by Tomasz Natkaniec)
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© 2021 Mathematical Institute Slovak Academy of Sciences
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Artikel in diesem Heft
- Regular Papers
- Quasi-decompositions and quasidirect products of Hilbert algebras
- Residuation in finite posets
- On a problem in the theory of polynomials
- Fekete-Szegö problem for starlike functions connected with k-Fibonacci numbers
- Mapping properties of the Bergman projections on elementary Reinhardt domains
- Lemniscate-like constants and infinite series
- On the Oscillation of second order nonlinear neutral delay differential equations
- Oscillation theorems for certain second-order nonlinear retarded difference equations
- De la Vallée Poussin inequality for impulsive differential equations
- Hs-Boundedness of a class of Fourier Integral Operators
- Dynamical behavior of a P-dimensional system of nonlinear difference equations
- Some inequalities for exponentially convex functions on time scales
- Impact of different types of non linearity on the oscillatory behavior of higher order neutral difference equations
- The sine extended odd Fréchet-G family of distribution with applications to complete and censored data
- A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations
- Simulations of nonlinear parabolic PDEs with forcing function without linearization
- An existence level for the residual sum of squares of the power-law regression with an unknown location parameter
- A relationship between the category of chain MV-algebras and a subcategory of abelian groups