Add to ORKGThrough an application of a remarkable result due to Mishev in 2018 concerning the inverses for a class of transformations of sequences of complex numbers, we obtain a very simple proof for a famous series for $\frac{1}{\pi}$ due to Ramanujan. We then apply Mishev's transform to provide proofs for a number of related hypergeometric identities, including a new and simplified proof for a family of series for $\frac{1}{\pi}$ previously obtained by Levrie via Fourier--Legendre theory. We generalize this result using Mishev's transform, so as to extend a result due to Guillera on a Ramanujan-like series involving cubed binomial coefficients and harmonic numbers.Comment: To appear in the Journal of the Ramanujan Mathematical Societ
ABSTRACT Srinivasa Ramanujan had established several hypergeometric series for the number 1/π out of...
We introduce classes of Ramanujan-like series for $\frac{1}{\pi}$, by devising methods for evaluatin...
We compute Ramanujan–Sato series systematically in terms of Thompson series and their modular equati...
AbstractA hypergeometric transformation formula is developed that simultaneously simplifies and gene...
AbstractIn this paper we derive a U(n) generalization of Ramanujan's 1Ψ1 summation directly from a r...
Ramanujan\u27s Master theorem states that, under suitable conditions, the Mellin transform of an alt...
During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of th...
We record $$ \binom{42}2+\binom{23}2+\binom{13}2=1192 $$ functional identities that, apart from bein...
. We state and prove a claim of Ramanujan. As a consequence, a large new class of Saalschutzian hype...
Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined b...
AbstractThis paper gives a brief exposition of several recent results obtained by the authors concer...
Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined b...
Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined b...
Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined b...
We resolve a family of recently observed identities involving 1/π using the theory of modular forms ...
ABSTRACT Srinivasa Ramanujan had established several hypergeometric series for the number 1/π out of...
We introduce classes of Ramanujan-like series for $\frac{1}{\pi}$, by devising methods for evaluatin...
We compute Ramanujan–Sato series systematically in terms of Thompson series and their modular equati...
AbstractA hypergeometric transformation formula is developed that simultaneously simplifies and gene...
AbstractIn this paper we derive a U(n) generalization of Ramanujan's 1Ψ1 summation directly from a r...
Ramanujan\u27s Master theorem states that, under suitable conditions, the Mellin transform of an alt...
During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of th...
We record $$ \binom{42}2+\binom{23}2+\binom{13}2=1192 $$ functional identities that, apart from bein...
. We state and prove a claim of Ramanujan. As a consequence, a large new class of Saalschutzian hype...
Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined b...
AbstractThis paper gives a brief exposition of several recent results obtained by the authors concer...
Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined b...
Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined b...
Ramanujan stated an identity to the effect that if three sequences {an}, {bn} and {cn} are defined b...
We resolve a family of recently observed identities involving 1/π using the theory of modular forms ...
ABSTRACT Srinivasa Ramanujan had established several hypergeometric series for the number 1/π out of...
We introduce classes of Ramanujan-like series for $\frac{1}{\pi}$, by devising methods for evaluatin...
We compute Ramanujan–Sato series systematically in terms of Thompson series and their modular equati...