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In this paper, we investigate and evaluate the analytical expressions for some definite integrals of Srinivasa Ramanujan in terms of Meijer’s  G -function by using the Laplace transforms ofsin⁡(β⁢x2){\sin(\beta x^{2})},cos⁡(β⁢x2){\cos(\beta x^{2})},x⁢sin⁡(β⁢x2){x\sin(\beta x^{2})}andx⁢cos⁡(β⁢x2){x\cos(\beta x^{2})}. In addition, we investigate a number of infinite summation formulas involving Meijer’s  G -function and closed-form evaluation of some related infinite series.

Consequences of Srinivasa Ramanujan integrals involving Meijer’s G -function