Results 11 to 20 of about 418 (20)
Semi-Finite Forms of Bilateral Basic Hypergeometric Series [PDF]
, 2005 We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas.
Chen, William Y. C., Fu, Amy M.
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On q-Laplace Transforms of the q-Bessel Functions [PDF]
, 2007 Mathematics Subject Classification: 33D15, 44A10, 44A20The present paper deals with the evaluation of the q-Laplace transforms of a product of basic analogues of the Bessel functions.
Kalla, S., Purohit, S.
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Zeros of Ramanujan Type Entire Functions
, 2016 In this work we establish some polynomials and entire functions have only real zeros. These polynomials generalize q-Laguerre polynomials $L_{n}^{(\alpha)}(x;q)$, while the entire functions are generalizations of Ramanujan's entire function $A_{q}(z)$, q-
Zhang, Ruiming
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Hankel Transform in Quantum Calculus and Applications [PDF]
, 2006 Mathematics Subject Classification: 44A15, 33D15, 81Q99This paper is devoted to study the q-Hankel transform associated with the third q-Bessel function called also Hahn-Exton function.
Haddad, Meniar
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A simple proof of Bailey's very-well-poised 6-psi-6 summation
, 2000 We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gauss' 2-F-1 summation and elementary series manipulations to give a simple proof of Dougall's 2-H-2 summation ...
Schlosser, M.
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Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets [PDF]
, 2007 Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60This paper aims to study the q-wavelets and the continuous q-wavelet transforms, associated with the q-Bessel operator for a fixed q ∈]0, 1[.
Bettaibi, Néji +2 more
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Proofs of Some Conjectures of Chan on Appell-Lerch Sums
, 2018 On page 3 of his lost notebook, Ramanujan defines the Appell-Lerch sum $$\phi(q):=\sum_{n=0}^\infty \dfrac{(-q;q)_{2n}q^{n+1}}{(q;q^2)_{n+1}^2},$$ which is connected to some of his sixth order mock theta functions. Let $\sum_{n=1}^\infty a(n)q^n:=\phi(q)$
Baruah, Nayandeep Deka +1 more
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On identities involving the sixth order mock theta functions
, 2009 We present q-series proofs of four identities involving sixth order mock theta functions from Ramanujan's lost notebook. We also show how Ramanujan's identities can be used to give a quick proof of four sixth order identities of Berndt and ...
Lovejoy, Jeremy
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Some explicit values for ratios of theta-functions [PDF]
, 2005 In his notebooks [9], Ramanujan recorded several values of thetafunctions.B. C. Berndt and L-C. Zhang [6], Berndt and H. H. Chan[5] have proved all these evaluations.
Madhusudhan, H.S., Mahadeva Naika, M.S.
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A generalization of starlike functions of order alpha [PDF]
, 2015 For every $q\in(0,1)$ and $0\le ...
Agrawal, Sarita, Sahoo, Swadesh K.
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