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References
Geometric properties of tau-confluent hypergeometric function
In the present investigation we first introduce normalized tau-confluent hypergeometric function phi(tau)(a; b; z) and then find sufficient conditions so that phi(tau)(a; b; z) have certain geometric properties like close-to-convexity and starlikeness in the open unit disk D. Upper bound of vertical bar phi(tau)(a; b; z)vertical bar and vertical bar phi(tau)(a; b; z)'vertical bar are also determined.
HOMOGENIZATION OF PERIODIC SCHRODINGER-TYPE EQUATIONS, WITH LOWER ORDER TERMS
In L-2(R-d;C-n), consider a selfadjoint matrix elliptic second order differential operator B-epsilon, 0 < epsilon <= 1, with periodic coefficients depending on x/epsilon. The principal part of the operator is given in a factorized form, the operator involves first and zero order terms. Approximation is found for the operator exponential e(-isB epsilon), s is an element of R, for small epsilon in the (H-tau -> L-2)-operator norm with a suitable r. The results are applied to study the behavior of the solution of the Cauchy problem for the nonstationary Schrodinger-type equation i partial derivative(s)u(epsilon) = B(epsilon)u(epsilon) + F. Applications to the magnetic Schrodinger equation and the two-dimensional Pauli equation with singular potentials are considered.