Additional results are obtained which center around expressions for the Laplace transforms of functions of the form <mml:math alttext="$k\left( t \right)F\left[ {g\left( t \right)} \right]$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>&#8201;F</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>g</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>. The finite Laplace transformation is involved in a number of the formulas. Examples involving several special cases of <mml:math alttext="$g$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>g</mml:mi></mml:math> and <mml:math alttext="$k$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math> are included.

International Journal of Mathematics and Mathematical Sciences

Substitution relations for Laplace transformations

Abstract

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