Approximation of Analytic Functions by Bessel’s Functions of Fractional Order
نویسندگان
چکیده
and Applied Analysis 3 The convergence of the power series ∑∞ m 0 amx m seems not to guarantee the existence of solutions to the inhomogeneous Bessel differential equation 1.4 . Thus, we adopt an additional condition to ensure the existence of solutions to the equation. Theorem 2.1. Let ν be a positive nonintegral number, and let ρ be a positive constant. Assume that the radius of convergence of power series ∑∞ m 0 amx m is at least ρ and there exists a constant σ > 0 satisfying the condition |am 2| ≤ m 2 σ2 |cm|, 2.1 for all sufficiently large integersm, where cm ⎧ ⎪ ⎪ ⎪ ⎪⎨ ⎪ ⎪ ⎪ ⎪⎩ − m/2 ∑
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