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Research Articles

Macdonald's identities and integral representations of products of Airy functions

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Pages 744-757 | Received 01 Dec 2019, Accepted 28 Feb 2020, Published online: 09 Mar 2020

References

  • Gradshteyn IS, Ryzhik IM. Table of integrals, series and products. 7th ed. New York: Academic Press; 2007.
  • Erdélyi A, Magnus W, Oberhettinger F, et al. Higher transcendental functions. Vol. 3. New York (NY): McGraw-Hill; 1955.
  • Vallee O, Soares M. Airy functions and applications to physics. London: Imperial College Press; 2004.
  • Ansari A, Masomi MR. Some results involving integral transforms of Airy functions. Integral Transform Spec Funct. 2015;26(7):539–549. doi: 10.1080/10652469.2015.1025072
  • Ansari A. The fractional Airy transform. Hacet J Math Stat. 2015;44(4):761–766.
  • Reid WH. Integral representations for products of Airy functions. Z Angew Math Phys. 1995;46:159–170. doi: 10.1007/BF00944750
  • Reid WH. Integral representations for products of Airy functions. Part 2: cubic products. Z Angew Math Phys. 1997;48:646–655. doi: 10.1007/PL00001481
  • Reid WH. Integral representations for products of Airy functions. Part 3: quartic products. Z Angew Math Phys. 1997;48:656–664. doi: 10.1007/PL00001482
  • Varlamov V. Semi-integer derivatives of the Airy functions and related properties of the Korteweg-de Vries-type equations. Z Angew Math Phys. 2008;59:381–399. doi: 10.1007/s00033-007-6074-2
  • Varlamov V. Fractional derivatives of products of Airy functions. J Math Anal Appl. 2008;337:667–685. doi: 10.1016/j.jmaa.2007.03.098
  • Varlamov V. Integrals involving products of Airy functions, their derivatives and Bessel functions. J Math Anal Appl. 2010;370:687–702. doi: 10.1016/j.jmaa.2010.05.004
  • Varlamov V. Differential and integral relations involving fractional derivatives of Airy functions and applications. J Math Anal Appl. 2008;348:101–115. doi: 10.1016/j.jmaa.2008.06.052
  • Varlamov V. Riesz fractional derivatives of the product of Airy transforms. Phys Scr. 2009;T136: 014004 (5pp). doi: 10.1088/0031-8949/2009/T136/014004
  • Dixon AL, Ferrar WL. Integrals for the product of two Bessel functions. Q J Math. 1933;os-4(1):193–208. doi: 10.1093/qmath/os-4.1.193
  • Dixon AL, Ferrar WL. Integrals for the product of two Bessel functions (II). Q J Math. 1933;os-4(1):297–304. doi: 10.1093/qmath/os-4.1.297
  • Ansari A. Green's function of two-dimensional time-fractional diffusion equation using addition formula of Wright function. Integral Transforms Spec Funct. 2019;30(4):301–315. doi: 10.1080/10652469.2018.1564750
  • Askari H, Ansari A. Airy functions and Riesz fractional trigonometric operators. Integral Transforms Spec Funct. 2018;29(8):585–604. doi: 10.1080/10652469.2018.1472593
  • Moslehi L, Ansari A. Integral representations of products of Airy functions related to fractional calculus. J Classical Anal. 2015;7(2):99–112. doi: 10.7153/jca-07-10
  • Ansari A, Masomi MR. Some integral identities for products of Airy functions using integral transforms. Asian Eur J Math. 2018;11(1):1850046.
  • Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and series. London: Gordon and Breach; 1993. (Direct Laplace transforms; vol. 4).
  • Apelblat A. Laplace transforms and their applications. New York: Nova Science Publishers; 2010.
  • Lebedev NN. Special functions & their applications. New York: Dover Publications; 1972.
  • Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and series. London: Gordon and Breach; 1993. (Inverse Laplace transforms; vol. 5).
  • Oberhettinger F. Tables of Bessel transforms. New York: Springer-Verlag; 1972.

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