This article defines a new operator called the q-Babalola convolution by using quantum calculus and of normalized analytic functions in open unit disk. We then study class bi-univalent defined disk associated with operator. The main results investigation include some upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szego inequalities class. Many applications finds are highlighted c...

This paper presents a new general subfamily NΣmu,v(η,μ,γ,ℓ) of the family Σm that contains holomorphic normalized m-fold symmetric bi-univalent functions in open unit disk D associated with Ruscheweyh derivative operator. For belonging to introduced here, we find estimates Taylor–Maclaurin coefficients am+1 and a2m+1, consequences results are discussed. The current findings both extend enhance ...

Subclasses of analytic and bi-univalent functions have been extensively improved utilized for estimating the Taylor–Maclaurin coefficients Fekete–Szegö functional. In this paper, we consider a certain subclass normalized functions. These inverses that possess continuation to an open unit disk are associated with orthogonal polynomials; namely, Gegenbauer polynomials satisfy subordination condit...

A relation between the zeros of the partial sums and the zeros of the corresponding tails of the Maclaurin series for e is established. This allows an asymptotic estimation of a quantity which came up in the theory of the Riemann zeta-function. Some new properties of the tails of e are also provided.

Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments Gi(z), Hi(z) and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series and asymptotic expansions. For real z comparison with a previous code by A.J. MacLeod (J. Comput. Appl. Math. 53 (1994)) is provided. 2000 Mathematics Subject Classification: 33C10, 65D20, 65D32, 3...

Using Hermite’s, i.e. the Euler-Maclaurin summation formula of order four, new approximations to Mathieu’s series S(x) ≡ ∑∞ k=1 2k (k2+x2) are obtained, which are more accurate than the approximations presented recently in the literature. Mathematics Subject Classification: 26D15, 33E20, 33F05, 40A05, 40A25, 65B10, 65B15, 65D20

the potential energy surface pes of (h2)2 dimer has been investigated, using five simple rigid rotor models. these models are called: head to head, symmetric side to side, l , steplike and t model. all calculations were done at two levels of ab initio  methods: mp2(full) and qcisd (t,full) using cc-pvtz basis set at singlet state of spin multiplicity. the results of scanning pes were then fitte...