(12⁢x)-ν-1⁢Hν⁡(x)=-12⁢π⁢ⅈ⁢∫-ⅈ⁢∞ⅈ⁢∞π⁢csc⁡(π⁢s)Γ⁡(32+s)⁢Γ⁡(32+ν+s)⁢(14⁢x2)s⁢ⅆ⁡s,