A note on the convergence of certain families of multiple hypergeometric series

Hải, Nguyễn Thanh; Marichev, O. I.; Srivástava, H. M.

doi:10.1016/0022-247x(92)90147-6

Cited by 34 publications

(9 citation statements)

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“…In this section, we define a general Hurwitz-Lerch Zeta function of two variables consisting of a double sequence of arbitrary complex numbers and then making an appeal to the convergence conditions of double series in ( [13], [14], [22], [23], [24], and [25]), we obtain convergence conditions for general Hurwitz-Lerch Zeta function of two variables and its related double zeta functions.…”

Section: The General Hurwitz-lerch Zeta Function Of Twomentioning

confidence: 99%

“…Now in last series of (9), use the Horn theorem due to [25] together with the formulae of ( [9], [10], [13], [14], [23], [25]) to get rational functions of m and n, given by…”

Section: The General Hurwitz-lerch Zeta Function Of Twomentioning

confidence: 99%

“…Again, in a similar way, as we have done in Eqns. (10) to (13), that if (s) > 0, |t| < 1, then for any large m or n,…”

Section: The General Hurwitz-lerch Zeta Function Of Twomentioning

confidence: 99%

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Certain Identities of a General Class of Hurwitz-Lerch Zeta Function of Two Variables

Pathan

Kumar²,

Sharma

2022

EJMS

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Section: The General Hurwitz-lerch Zeta Function Of Twomentioning

confidence: 99%

“…Now in last series of (9), use the Horn theorem due to [25] together with the formulae of ( [9], [10], [13], [14], [23], [25]) to get rational functions of m and n, given by…”

Section: The General Hurwitz-lerch Zeta Function Of Twomentioning

confidence: 99%

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Certain Identities of a General Class of Hurwitz-Lerch Zeta Function of Two Variables

Pathan

Kumar²,

Sharma

2022

EJMS

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“…In fact, in Legendre's normal form, the incomplete elliptic integrals of the first and second kind (with modulus |k|and amplitude ϕ) are defined by (cf., e.g., [5] and [12]; see also [2,Chapter 17], [11,Chapter 9] and [10, Vol. II, Chapter 13]):…”

Section: B L Chaurasia and Ravi Shanker Dubeymentioning

confidence: 99%

Definite integrals of generalized certain class of incomplete elliptic integrals

Dubey¹,

Chaurasia

2013

Tamkang J. Math.

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Abstract. Elliptic-integral have their importance and potential in certain problems in radiation physics and nuclear technology, studies of crystallographic minimal surfaces, the theory of scattering of acoustic or electromagnetic waves by means of an elliptic disk, studies of elliptical crack problems in fracture mechanics. A number of earlier works on the subject contains remarkably large number of general families of elliptic-integrals and indeed also many definite integrals of such families with respect to their modulus (or complementary modulus) are known to arise naturally. Motivated essentially by these and many other potential avenues of their applications, our aim here is to give a systematic account of the theory of a certain family of generalized incomplete elliptic integrals in a unique and generalized manner. The results established in this paper are of manifold generality and basic in nature. By making use of the familiar Riemann-Liouville fractional differ integral operators, we establish many explicit hypergeometric representations and apply these representation in deriving several definite integrals pertaining to their, not only with respect to the modulus (or complementary modulus), but also with respect to the amplitude of generalized incomplete elliptic integrals involved therein.

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“…A:B:C (x, y) converges absolutely on |x| ≤ 1 and |y| ≤ 1 when the parameters satisfy the three conditions [7] Re…”

mentioning

confidence: 99%

Hypergeometric expressions of $L$-values for a Borweins theta product of weight $3$

Ito¹

2022

Preprint

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A note on the convergence of certain families of multiple hypergeometric series

Cited by 34 publications

References 1 publication

Certain Identities of a General Class of Hurwitz-Lerch Zeta Function of Two Variables

Certain Identities of a General Class of Hurwitz-Lerch Zeta Function of Two Variables

Definite integrals of generalized certain class of incomplete elliptic integrals

Hypergeometric expressions of $L$-values for a Borweins theta product of weight $3$

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