This is the fifth and final volume that the authors have written in their examination of all the
claims made by S. Ramanujan in The Lost Notebook and Other Unpublished Papers …

1 X nD 1 qn2 xn; where jqj< 1 and 0< jxj< 1; or a generalization or specialization of such a
series. Theta functions were studied extensively by Ramanujan and form the central theme …

We consider the order parameter u=⟨ Tr ϕ 2⟩ as a function of the running coupling constant
τ∈ H of asymptotically free N= 2 QCD with gauge group SU (2) and N f≤ 3 massive …

361 Rational analogues of Ramanujan’s series for 1/π† Page 1 Math. Proc. Camb. Phil. Soc.
(2012), 153, 361–383 c Cambridge Philosophical Society 2012 doi:10.1017/S0305004112000254 …

The author gives the full list of his conjectures on series for powers of $\pi $ and other
important constants scattered in some of his public papers or his private diaries. The list …

Two new sequences, which are analogues of six sporadic examples of D. Zagier, are
presented. The connection with modular forms is established and some new series for 1/π …

Full article: Super congruences for two Apéry-like sequences Skip to Main Content Taylor
and Francis Online homepage Taylor and Francis Online homepage Log in | Register Cart 1.Home …

Via symbolic computation we deduce 97 new type series for powers of $\pi $ related to
Ramanujan-type series. Here are three typical examples: $$\sum_ {k= 0}^\infty\frac {P …

We find new representations, in terms of constant terms of powers of Laurent polynomials,
for all the 15 sporadic Apéry-like sequences discovered by Zagier, Almkvist-Zudilin and …

In 1951, Brafman derived several “unusual” generating functions of classical orthogonal
polynomials, in particular, of Legendre polynomials Pn (x). His result was a consequence of …