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- W4313893709 abstract "Abstract 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 of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>sin</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>β</m:mi> <m:mo></m:mo> <m:msup> <m:mi>x</m:mi> <m:mn>2</m:mn> </m:msup> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {sin(beta x^{2})} , <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>cos</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>β</m:mi> <m:mo></m:mo> <m:msup> <m:mi>x</m:mi> <m:mn>2</m:mn> </m:msup> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {cos(beta x^{2})} , <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>x</m:mi> <m:mo></m:mo> <m:mrow> <m:mi>sin</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>β</m:mi> <m:mo></m:mo> <m:msup> <m:mi>x</m:mi> <m:mn>2</m:mn> </m:msup> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {xsin(beta x^{2})} and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>x</m:mi> <m:mo></m:mo> <m:mrow> <m:mi>cos</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>β</m:mi> <m:mo></m:mo> <m:msup> <m:mi>x</m:mi> <m:mn>2</m:mn> </m:msup> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {xcos(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." @default.
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- W4313893709 date "2023-01-10" @default.
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- W4313893709 title "Consequences of Srinivasa Ramanujan integrals involving Meijer’s <i>G</i>-function" @default.
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- W4313893709 doi "https://doi.org/10.1515/anly-2022-1059" @default.
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