This paper studies an extended Bessel function of the form [Formula: see text] Representation formulations for [Formula: see text] are derived in terms of the parametersa,b, and p. An important consequence is the derivation of an [Formula: see text]-order differential equation satisfied by the function [Formula: see text]. Interesting functional inequalities are established, particularly for the case [Formula: see text], and [Formula: see text]. Monotonicity properties of [Formula: see text] are also studied for non-positive c. Log-concavity and log-convexity properties in terms of the parametersdandpare respectively investigated for the closely related function [Formula: see text] which leads to direct and reverse Turán-type inequalities.
Metastasis of an atrial myxoma to the brain is extremely rare. Thus far there are only 17 cases reported, including our present case. Most of the brain metastases manifest only in 3 to 6 decades, after an average time frame of one to two years after surgical removal of parental tumour. We present a case of brain metastases of atrial myxoma in a teenager of the youngest age among all reported cases, unusually as early as 15 years old. The progress of the metastatic process had been insidious for three years after heart surgery, The imaging demonstrated a rather sizeable tumour by the time when the patient is symptomatic. The location of the metastatic tumour is anyhow superficial to the cortical surface, enabling complete surgical excision of the tumour easily achievable with favourable outcome.