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On fractional calculus of A2n+1(x) function

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  • Ansari, Alireza
  • Askari, Hassan

Abstract

In this article, we consider the 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) function, A2n+1(x) wavelets and integral and series identities. Moreover, the A2n+1(x) polynomials are derived and bi-orthogonality properties with their associated functions are obtained.

Suggested Citation

  • Ansari, Alireza & Askari, Hassan, 2014. "On fractional calculus of A2n+1(x) function," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 487-497.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:487-497
    DOI: 10.1016/j.amc.2014.01.058
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    References listed on IDEAS

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    1. Aimé Lachal, 2012. "A Survey on the Pseudo-process Driven by the High-order Heat-type Equation $\boldsymbol{\partial/\partial t=\pm\partial^N\!/\partial x^N}$ Concerning the Hitting and Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 549-566, September.
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    Cited by:

    1. Marchione, Manfred Marvin & Orsingher, Enzo, 2023. "Pseudoprocesses related to higher-order equations of vibrations of rods," Statistics & Probability Letters, Elsevier, vol. 199(C).

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