On fractional calculus of A2n+1(x)A2n+1(x) function

In this article, we consider the A2n+1(x)A2n+1(x) function (the generalized Airy function)A2n+1(x)=∫0∞coszx+(-1)n+1z2n+12n+1dzand find some properties of this function and its derivatives. These properties are included in integral representations for product of A2n+1(x)A2n+1(x) function, A2n+1(x)A2n+1(x) wavelets and integral and series identities. Moreover, the A2n+1(x)A2n+1(x) polynomials are derived and bi-orthogonality properties with their associated functions are obtained.