# Evaluation of certain indefinite integrals.

[section] 1. Introduction and preliminaries

The Pochhammer's symbol or Appell's symbol or shifted factorial or rising factorial or generalized factorial function is defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where 6 is neither zero nor negative integer and the notation [GAMMA] stands for Gamma function.

Generalized Gaussian Hypergeometric Function: Generalized ordinary hypergeometric function of one variable is defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

or

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where denominator parameters [b.sub.1], [b.sub.2], ... , [b.sub.B] are neither zero nor negative integers and A, B are non-negative integers.

[section] 2. Main indefinite integrals

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Constant. (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Constant. (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Constant. (5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Constant. (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Constant. (7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Constant. (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Constant. (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Constant. (10)

[section] 3. Derivation of the integrals

Applying the same method which is used in [4], integrals will be established.

[section] 4. Applications

The integrals which are presented here are very special integrals. These are applied in the field of engineering and other allied sciences.

[section] 5. Conclusion

In our work we have established certain indefinite integrals involving Hypergeometric function. However, one can establish such type of integrals which are very useful for different field of engineering and sciences by involving these integrals. Thus we can only hope that the development presented in this work will stimulate further interest and research in this important area of classical special functions.

References

[1] Milton Abramowitz and Irene A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, 1970.

[2] Hancock Harris, Elliptic integrals, John Wiley&sons, Inc., 1917.

[3] Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert and C. W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, 2010.

[4] M. I. Qureshi, Salahuddin, M. P. Chaudhary and K. A. Quraishi, Evaluation of Certain Elliptic Type Single, Double Integrals of Ramanujan and Erdelyi, J. Mathematics Research, 2(2010), 148-156.

Salahuddin

P. D. M College of Engineering, Bahadurgarh, Haryana, India E-mail: vsludn@gmail.com sludn@yahoo.com