Abstract: In this paper, we proved transformation formulas for nonterminating very well-poised 4Φ3-series, 4Ψ4-series, 6Φ5-series, 6Ψ6-series, 8Φ7-series and 8Ψ8-series, which utilize the method of ...

We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q-series based on our expectation formula. Although these formulas in themselves are ...

Trigonometric sums and summation formulas have long served as essential tools for elucidating periodic phenomena across mathematics and the physical sciences. These techniques entail the explicit ...

ABSTRACT: Very recently Atash and Al-Gonah [1] derived two extension formulas for Lauricella’s function of the second kind of several variables and . Now in this research paper we derive two families ...

Abstract: System of Synthesis and Verification of Hardware Models-Formulas for Series Summation in Reproducing Kernel Hilbert Space (RKHS) which allows to carry out input of the description of the ...

Summation, also known as sigma notation, is a mathematical concept used to represent the addition of a sequence of numbers or terms. It is widely employed in various fields such as mathematics, ...