A Study of Psi-Function

Y. Pragathi Kumar, B. Satyanarayana


The aim of this paper is to introduce a new generalization of the well-known, interesting and useful Fox \(H\)-function and \(I\)-function into generalized function, namely, the Psi-function. From which authors obtained I-function defined by Saxena [17] and Rathie [8]. Convergent conditions, elementary properties, and special cases have also been given.


\(I\)-function; \(H\)-function; Mellin transform; Laplace transform; General class of polynomials; Struve’s function

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T. W. Anderson, An Introduction to Multi Variable Statistical Analysis, John Wiley, New York (1984), http://www.ru.ac.bd/stat/wp-content/uploads/sites/25/2019/03/301_03_Anderson_An-Introduction-to-Multivariate-Statistical-Analysis-2003.pdf.

A. Erdelyi, Table of Integral Transforms, Vol. I, McGraw-Hill Book Co., New York (1953). [3] C. Fox, The G and H-functions as symmetrical Fourier kernels, Transactions of American Mathematical Society 98, 196 (1961), 395 – 429.

I. S. Gradshteyin and I. M. Ryzhik, Table of Integrals, Series and Products, 6/e, Academic Press, New Delhi (2001).

J. Mishra and N. Pandey, An integral involving general class of polynomials with I-function, International Journal of Scientific and Research Publications 3(1) (2013), 1 – 3, http://citeseerx.ist.psu.edu/viewdoc/download?doi=

Y. L. Luke, The Special Functions and Their Approximations, Vol. 1, Academic Press, New York (1969), https://ia601608.us.archive.org/0/items/in.ernet.dli.2015.141299/2015.141299.The-Special-Functions-And-Their-Approximations-Vol-1.pdf.

M. Garg and S. Mittal, On a new unified integral, Proceedings of the Indian Academy of Sciences - Mathematical Sciences 114(2) (2004), 99 – 101, DOI: 10.1007/BF02829845.

A. K. Rathie, A new generalization of generalized hypergeometric functions, Le Mathematiche, I, LII Fasc. II (1997), 297 – 310, https://arxiv.org/ftp/arxiv/papers/1206/1206.0350.pdf.

B. Satyanarayana and Y. P. Kumar, Integral transform involving the product of general class of polynomials, Struve’s function, H-function of one variable and H-function of ‘r’ variables, Applied Mathematical Sciences 5(57) (2011), 2831 – 2838, http://www.m-hikari.com/ams/ams-2011/ams-57-60-2011/pragathiAMS57-60-2011.pdf.

B. Satyanarayana, P. Y. Kumar, N. Srimannarayana and B. V. Purnima, Solution of boundary value problems involving I-function and Struve’s function, International Journal of Recent Technology and Engineering 8(3) (2019), 411 – 415, https://www.ijrte.org/wp-content/uploads/papers/v8i3/C4205098319.pdf.

B. Satyanarayana, P. Y. Kumar and B. V. Purnima, Mellin and Laplace transforms involving product of Struve’s function and I-function of two variables, Arya Bhatta Journal of Mathematics and Informatics 10(1) (2018), 17 – 24, https://2164ee62-242c-4927-ad0ce25decce551c.filesusr.com/ugd/1ee7d3_24062fd20dbd485c9922cf89322f9178.pdf.

P. Jain, A. Gupta and V. P. Saxena, Multiple integral involving I-function and Bessel-Maitland functions, International Journal of Mathematics Trends and Technology 39(3) (2016), 232 – 237, https://ijmttjournal.org/2016/Volume-39/number-3/IJMTT-V39P529.pdf.

Y. P. Kumar, A. Mabrahtu, B. V. Purnima and B. Satyanarayan, Mellin and Laplace transforms involving the product of extended general class of polynomials and I-function of two variables, International Journal of Mathematical Sciences and Engineering Applications. 10(III) (2016), 143 – 150, http://www.ascent-journals.com/IJMSEA/Vol10No3/13-kumar.pdf.

Y. P. Kumar, L. P. Rao and B. Satyanarayana, Derivatives involving I-function of two variables and general class of polynomials, British Journal of Mathematics and Computer Science 9(5) (2015), 446 – 452, https://doi.org/10.9734/BJMCS/2015/17700.

Y. P. Kumar and B. Satyanarayana, Integral transform involving the product of general class of polynomials and H-function of two variables, Arya Bhatta Journal of Mathematics and Informatics 3(1) (2011), 43 – 48.

V. P. Saxena, A formal solution of certain new pair of dual integral equations involving H-functions, Proceedings of the National Academics of Science, India 52(A) III (1982), p. 336 – 375.

V. P. Saxena, The I-function, Anamaya Publishers, New Delhi (2008).

H. M. Srivastava, K. C. Gupta and S. P. Goyal, The H-functions of One and Two Variables with Applications, South Asian Publishers, New Delhi (1982).

V. Jat, V. P. Saxena and P. L. Sanodia, On certain special cases of existence conditions of I-function, Jnanabha 48(1) (2018), 72 – 78, http://docs.vijnanaparishadofindia.org/jnanabha/jananabha_volume_48_v1_2018/jnanabha_volume_48_v1_2018.pdf.

DOI: http://dx.doi.org/10.26713%2Fjims.v12i2.1340

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