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A remarkably large number of integrals involving a product of certain combinations of Bessel functions of several kinds as well as Bessel functions, themselves, have been investigated by many authors. Motivated the works of both Garg and Mittal and Ali, very recently, Choi and Agarwal gave two interesting unified integrals involving the Bessel function of the first kind $J_{\nu}(z)$. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present two generalized integral formulas involving a product of Bessel functions of the first kind, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. Some interesting special cases and (potential) usefulness of our main results are also considered and remarked, respectively.
#Gamma function
#Hypergeometric function $_2F_1$
#generalized hypergeometric function $_pF_q$
#generalized
#wright) hypergeometric functions $_p{Psi}_q$
#generalized hypergeometric series
#generalized Lauricella series in several variables
#cosine and sine trigonometric functions
#Bessel function of the first kind
#Oberhettinger's integral formula
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참고문헌 (21)
참고문헌 신청
M. Abramowitz / 1972 / Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Tenth Printing, National Bureau of Standards / Dover Publications
G. E. Andrews / 1999 / Special Functions / Cambridge University Press
S. Ali / 2012 / On some new unified integrals / Adv. Comput. Math. Appl 1(3):151~153
W. N. Bailey / 1936 / Some infinite integrals involving Bessel functions / Proc. London Math. Soc 40(2):37~48
Y. A. Brychkov / 2008 / Handbook of Special Functions, Derivatives, Integrals, Series and Other Formulas / CRC Press, Taylor & Francis Group
G. E. Andrews / 1999 / Special Functions / Cambridge University Press
S. Ali / 2012 / On some new unified integrals / Adv. Comput. Math. Appl 1(3):151~153
W. N. Bailey / 1936 / Some infinite integrals involving Bessel functions / Proc. London Math. Soc 40(2):37~48
Y. A. Brychkov / 2008 / Handbook of Special Functions, Derivatives, Integrals, Series and Other Formulas / CRC Press, Taylor & Francis Group
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