A four parameter integral identity and a few consequences
The identity \[ _0^∞ e^-α xe^-ax^2+2β x+b^2 x^2+2β x+b^2 dx = _0^∞ e^-β xe^-bx^2+2α x+a^2 x^2+2α x+a^2 dx \] is derived, applied to the Struve function \(H_0\) and used to deduce the reduction formula \[ _0^∞ F(x^2+2β x+b^2+x)x^2+2β x+b^2 dx = _0^∞ f(t)e^β t E_1[(β+b)t] dt, \] where \(F\) is arbitrary. , journal=Scientia Series A: Mathematical Sciences, author=Glasser, M.L., year=2025, month=Feb., pages=9–12