As samples for possible applications of these lemmas, we provide several A_n extensions of Bailey's 2-psi-2 transformations, and several A_n extensions of a particular 2-psi-2 summation.doi:10.1216/rmjm/1030539696Stephen C. MilneMichael Schlosser...
Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely ...
Ramanujan Sums in the Context of Signal Processing--Part II: FIR Representations and Applications The mathematician Ramanujan introduced a summation PP Vaidyanathan - 《IEEE Transactions on Signal Processing A Publication of the IEEE Signal Processing Society》 被引量: 30发表: 2014年 ...
q-Series with Applications to Combinatorics, Number Theory, and Physics H. Hardy described what we now call Ramanujan's famous \\(_1\\psi_1\\) summation theorem as "a remarkable formula with many parameters." This is now one of the fundamental theorems of the subject.Despite humble ...
Munshi, R.: A Note on Burgess Bound, Geometry, Algebra, Number Theory, and Their Information Technology Applications, vol. 251, pp. 273–289. Springer, Cham (2018) Petrow, I., Young, M.P.: The fourth moment of DirichletL-functions along a coset and the Weyl bound,arXiv:1908.10346 ...
(1.1) where theq-Pochhammer symbol is defined by The above infinite product on the right-hand side withoutin the denominator appears in the well-known generalized Rogers–Ramanujan identities of Andrews, Bressoud, and Gordon [1,14,24]. As briefly mentioned earlier, this infinite product can al...
0 n,m The resulting bracket series has more summation indices than brackets. The choice of n as a free variable, gives m∗ = −n − s and Rule 2 produces the convergent series (9.9) ∞ (−1)n n! Γ(n + s) = Γ(s)1F0 s − −1 Γ(s) = 2s . n=0 Symmetry ...
[Generalizations of Kummer's second theorem with applications, Comput. Math. Math. Phys. 50(3) (2010), pp. 387–402] and extension of Gauss' summation theorem available in the literature. Several special cases that are closely related to Ramanujan's results are also given....
A unified approach to the summation and integration formulas for q-hypergeometric functions I The most basic summation formula in the theory of q -hypergeometric functions is the well-known q -binomial formula. Not so well-known is the fact that the... M Rahman,S Suslov - 《Journal of Sta...
It is well known that F(a,b;c;x) has wide applications in many branches of mathematics and physics. Many elementary and special functions in mathematical physics are the particular or limiting cases of the Gaussian hypergeometric function. F(a,b;c;x) is said to be zero-balanced if c=...