论文标题
Bessel Zeta功能
The Bessel zeta function
论文作者
论文摘要
研究了贝塞尔Zeta功能的两种表示。使用轮廓集成构建不完整的表示形式，并对霍金斯（Hawkins）引起的积分表示（分析性持续）产生两个无限序列。以参数的整体值进行评估的新表示形式产生与已知结果（值，斜率和极结构）一致的结果。毫不奇怪，发现所研究的两种表示的系数相似，但功能形式略有不同。通过允许Bessel函数的顺序达到1/2，可以获得Riemann Zeta函数的表示。
Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two infinite series. This new representation, evaluated at integer values of the argument, produces results that are consistent with known results (values, slope, and pole structure). Not surprisingly, the two representations studied are found to have similar coefficients but a slightly different functional form. A representation of the Riemann zeta function is obtained by allowing the order of the Bessel function to go to 1/2.
