Voir la notice de l'article provenant de la source International Scientific Research Publications
Shah, S. A. H. 1 ; Mubeen, S. 1
@article{JNSA_2022_15_2_a2, author = {Shah, S. A. H. and Mubeen, S.}, title = {Laplace transform of some special functions in terms of generalized {Meijer} {\(G\)-functions}}, journal = {Journal of nonlinear sciences and its applications}, pages = {109-122}, publisher = {mathdoc}, volume = {15}, number = {2}, year = {2022}, doi = {10.22436/jnsa.015.02.03}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.02.03/} }
TY - JOUR AU - Shah, S. A. H. AU - Mubeen, S. TI - Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions JO - Journal of nonlinear sciences and its applications PY - 2022 SP - 109 EP - 122 VL - 15 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.02.03/ DO - 10.22436/jnsa.015.02.03 LA - en ID - JNSA_2022_15_2_a2 ER -
%0 Journal Article %A Shah, S. A. H. %A Mubeen, S. %T Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions %J Journal of nonlinear sciences and its applications %D 2022 %P 109-122 %V 15 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.02.03/ %R 10.22436/jnsa.015.02.03 %G en %F JNSA_2022_15_2_a2
Shah, S. A. H.; Mubeen, S. Laplace transform of some special functions in terms of generalized Meijer \(G\)-functions. Journal of nonlinear sciences and its applications, Tome 15 (2022) no. 2, p. 109-122. doi : 10.22436/jnsa.015.02.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.02.03/
[1] The evaluation of integrals of Bessel functions via $G$-function identities, J. Comput. Appl. Math., Volume 64 (1995), pp. 283-290
[2] On some properties of $\beta$-Laplace integral transform, J. Math. Computer Sci., Volume 23 (2021), pp. 315-320
[3] Meijer $G$-function: A Gentle Introduction, Notices Amer. Math. Soc., Volume 60 (2013), pp. 866-872
[4] Certain unified integrals associated with Bessel functions, Bound. Value Probl., Volume 2013 (2013), pp. 1-9
[5] On hypergeometric functions and pochhammer $k$-symbol, Divulg. Mat., Volume 15 (2007), pp. 179-192 | EuDML | Zbl
[6] $q,k$-Generalized Gamma and Beta Functions, J. Nonlinear Math. Phys., Volume 12 (2008), pp. 118-134
[7] Introduction to the theory and applications of the Laplace transformation, Springer-Verlag, New York, 1970
[8] Higher Transcendental Functions, Vol. I, McGraw-Hill Book Co., New York-Toronto-London, 1953
[9] Tables of Integral Transforms, Vol. I, McGraw-Hill Book Co., New York-Toronto-London, 1954
[10] Higher Transcendental Function, Vol. III, McGraw-Hill Book Company, New York-Toronto-London, 1955
[11] Hilfer-Prabhakar derivatives and some applications, Appl. Math. Comput., Volume 242 (2014), pp. 576-589
[12] Table of integrals, series, and products, Academic Press, San Diego, 2007
[13] Properties and inequalities of generalized $k$-gamma, beta and zeta functions, Int. J. Contemp. Math. Sci., Volume 5 (2010), pp. 653-660
[14] The Special Functions and Their Approximations, Academic Press, New York-London, 1969
[15] Determining the $k$-generalized gamma function $\Gamma_k(x)$ by functional equations, Int. J. Contemp. Math. Sci., Volume 4 (2009), pp. 1037-1042
[16] Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Springer-Verlag, New York, 1973
[17] The $H$-Function, Springer, New York, 2010
[18] Uber Whittakersche Bezw. Besselsche Funktionen und deren Produkte, Nieuw. Arch. Wiskunde, Volume 18 (1936), pp. 10-39
[19] Multiplikationstheoreme fur die Funktion $G^{m,n}_{p,q}(z)$, Nederl. Akad. Wetensch. Proc. Ser. A, Volume 44 (1941), pp. 1062-1070
[20] Neue Integralstellungen fur Whittakersche Funktionen I, Nederl. Akad. Wetensch. Proc. Ser. A, Volume 44 (1941), pp. 81-92
[21] Expension theorems for the $G$-function, V. Nederl. Akad. Wetensch. Proc. Ser. A. 56 = Indagationes Math., Volume 15 (1953), pp. 349-397
[22] $k$-fractional integrals and application, Int. J. Contemp. Math. Sci., Volume 7 (2012), pp. 89-94
[23] Extension of $k$-gamma, $k$-beta functions and $k$-beta distribution, J. Math. Anal., Volume 7 (2016), pp. 118-131
[24] Certain inequalities involving the $k$-Struve function, J. Inequal. Appl., Volume 2017 (2017), pp. 1-8
[25] Generalized hypergeometric $k$-functions via $(k,s)$-fractional calculus, J. Nonlinear Sci. Appl., Volume 10 (2017), pp. 1791-1800
[26] Certain Gronwall type inequalities associated with Riemann-Liouville $k$-and hadamard $k$-fractional derivatives and their applications, East Asian Math. J., Volume 34 (2018), pp. 249-263
[27] Handbook of Laplace Transformation, Prentice-Hall, Englewood Cliffs, 1960
[28] Hypergeometric Functions, Acta Math., Volume 94 (1955), pp. 289-349
[29] Tables of Laplace Transforms, Springer-Verlag, New York-Heidelberg, 1973
[30] A $G$-function form of radial states in carbon and hydrogen atoms: absorption or emission of radiation, Adv. Stud. Theor. Phys., Volume 9 (2015), pp. 145-154
[31] Integrals and Series, Vol. 3, Gordon and Breach Science Publishers, New York, 1990
[32] Integrals and Series, Vol. 4, Gordon and Breach Science Publishers, New York, 1992
[33] Integrals and Series, Vol. 5, Gordon and Breach Science Publishers, New York, 1992
[34] Laplace Transforms of Some Special Functions of Mathematical Physics Using Mellin-Barnes Type Contour Integration, Int. J. Math. Stat. Invent., Volume 3 (2015), pp. 21-34
[35] The Extended $k$-Mittag-Leffler Function and Its Properties, Proc. Jangjeon Math. Soc., Volume 21 (2018), pp. 487-495
[36] Inequalities Involving Extended $k$-Gamma and $k$-Beta Functions, Proc. Jangjeon Math. Soc., Volume 21 (2018), pp. 143-153
[37] Special functions, Macmillan Co., New York, 1960 | Zbl | DOI
[38] Modified Laplace transform and its properties, J. Math. Computer Sci., Volume 21 (2020), pp. 127-135
[39] Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966
Cité par Sources :