Properties determining optimal behavior of continuous analytic wavelet functions are investigated, and wavelet functions nearly obtaining such behavior are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a highly flexible family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a unique interpr...

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0 F 3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the ano...

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anoma...

Special functions such as hypergeometric, zeta, Bessel, Whittaker, Struve, Airy, Weber-Hermite and Mittag-Leffler are obtained a solution to complex differential equations in engineering, science technology. In this work, generalized Euler-type integrals involving four parameters function proposed. Some special cases of type that corresponding well-known results the literature also inferred.

We present an efficient implementation of hypergeometric functions in arbitraryprecision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U -function) are supported for unrestricted complex parameters and argument, and by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, ...