The Natural Logarithmic Transformation and its Applications


Emad Kuffi,Elaf Sabah Abbas,



Boundary value, changing the measurement theorem,derivative transformation theorem, existence theorem, first transition theore,logarithmi integral transformation,


In this paper, a new integral transformation is proposed, where the transformation kernel is the natural logarithmic function 𝑙𝑛(∝ 𝑥), ∝> 0, 𝑥 > 0 , the transformation interval is the closed interval 􁉂 􀬵 ∝ , 1􁉃, and the range of its kernel 𝑙𝑛(∝ 𝑥) is the entire set of the real numbers (−∞ < 𝑙𝑛(∝ 𝑥) < ∞). The wide range of the kernel for the proposed transformation giving it a wider usage from the other transformations such as Laplace transformation which its kernel is (𝑒􀬿􀰈􀯫 )and its range includes the natural numbers only ((𝑒􀬿􀰈􀯫) > 0). The proposed integral transformation is called “the logarithmic integral transformation” based on the kernel of the transformation. Some properties and theorems are presented for this new transformation.


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