广义半整数不完全伽玛函数及其应用

The generalized incomplete Gamma function for half-integers and its application

对广义不完全伽玛函数Γ(α,z;b)的性质进行了研究并得到一系列结果.特别是Γ(α,z;b),α=n+1/2,n=0,±1,±2,…的闭形式仅由误差函数表示.通过递推公式,给出了Γ(α±n,z;b),n=1,2,…的显式表示.

In this paper,a study is conducted on the series expansion of the generalized incomplete Gamma functionΓ（α,z;b）,the findings of which shows that the new closed form ofΓ（α,z;b）,α=n＋1/2,n=0,±1,±2,…is only represented by the error function.Finally,through the recurrence formula,the explicit representation ofΓ（α±n,z;b）,n=1,2,…is brought forth.