The Algebraic Derivative Applied to Laplace’s Differential Equation

  • K. Yosida
Part of the Applied Mathematical Sciences book series (AMS, volume 55)


Pierre Simon Laplace (1749–1827) in his treatise “Théorie analytique des probabilités” of 1817 considered a differential equation which now carries his name and which may be written as
$$ \left( {{a_2}t + {b_2}} \right)y''\left( t \right) + \left( {{a_1}t + {b_1}} \right)y'(t) + \left( {{a_0}t + b} \right)y\left( t \right) = 0, $$
where the a’s and b’s are given complex numbers with a2≠ 0.


Complex Number Ferential Equation Operational Calculus Linear Ordinary Differential Equation Convolution Theorem 
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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • K. Yosida
    • 1
  1. 1.Kamakura 247Japan

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