Convexity Properties of Special Functions and Their Zeros
نویسنده
چکیده
Convexity properties are often useful in characterizing and nding bounds for special function and their zeros as well as in questions concerning the existence and uniqueness of zeros in certain intervals In this survey paper we describe some work related to the gamma function the q gamma function Bessel and cylinder functions and the Hermite function Introduction Many inequalities for special functions are statements about the positivity or monotonicity of certain quantities Some deeper results refer to higher monotonic ity or even complete monotonicity i e the derivatives of successive derivatives or di erences alternate in sign An intermediate kind of result refers to convexity Convexity is often used to characterize certain special functions such as the gamma function Convexity properties are often useful in obtaining bounds for zeros In other cases such properties can be used to prove existence or uniqueness of zeros in certain intervals In this expository paper we give examples of these ideas Gamma and Related Functions THE GAMMA FUNCTION The gamma function is usually de ned for Re z by Euler s integral
منابع مشابه
Convexity Properties of Special Functions
Convexity properties are often useful in characterizing and nding bounds for special function and their zeros, as well as in questions concerning the existence and uniqueness of zeros in certain intervals. In this survey paper, we describe some work related to the gamma function, the q-gamma function, Bessel and cylinder functions and the Hermite function.
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