Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions.

In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hypergeometric function, and a determinant. These results generalize known ones in combinatorics.

Neuroendoscopy-Assisted Evacuation of Chronic Subdural Hematoma with Mixed CT Density Through A Novel Small Bone Flap.

OBJECTIVE: Chronic subdural hematoma (CSDH) is a common neurosurgical condition with an increasing incidence and favorable prognosis. Surgery is the standard treatment for CSDH, and bur hole evacuation is the most widely employed technique. However, if mixed computed tomography (CT) density is found, burr hole hematoma evacuation is prone to recurrence. Endoscopic examination of the hematoma cavity provides a novel strategy. Here, we present a modification of burr hole evacuation by using neuroendoscopy through a novel small trapezoid bone flap and assess the advantages and risks of the procedure. METHODS: Twenty-five patients diagnosed with CSDH of mixed CT density were included in this study. Radiographic, epidemiologic, and clinical data were collected and analyzed. In all procedures the burr hole was replaced by a small trapezoidal cross-sectional bone flap, ∼2 cm in diameter. Neuroendoscopy was employed after the subdural cavity was cleaned and drained. The CSDH cavity was inspected thoroughly. If a blood clot, septa, stretching of cortical vessels, or intraluminal trabecular structures with active bleeding were found, the surgeon aspirated the region with a syringe pipe and/or used bipolar electrocoagulation. RESULTS: All 25 patients who received 26 neuroendoscopy-assisted operations achieved favorable clinical outcomes. The recurrence rate was 4%. The average operation time was slightly increased compared with the traditional burr hole evacuation due to the use of the neuroendoscope and eventual subsequent treatment. CONCLUSION: Neuroendoscopy provides excellent illumination and vision when a small bone flap is employed. The main advantages of this technique include the precise treatment of structures which are related with progression and recurrence of CSDH, and the minimally invasive nature of the procedure.