Unicity of Entire Functions That Share One Value With Their Linear Differential Polynomials

Let f be a nonconstant entire function, let a be a finite nonzero complex number, and let L(integral) = integral ((k)) + a(k-1) integral((k-1)) + ... + a1 integral' + a(0) integral, where k >= 2 is a positive integer, a(j) (j = 0, 1, 2,..., k-1) are constants. Suppose that f (z) = a double right arrow f '(z) = a, and f '(z) = a double right arrow L (f)(z) = L'(f)(z) = a. Then, if a(0) not equal 1, then either f (z) = 1/Ae(1-a0e) Z + a or f (z) = A e(z), where A is a nonzero constant; if a(0) = 1, then L (f) = f.