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Logarithmic Transform

The inverse transform

sum_(n=1)^infty(a_nx^n)/(n!)=ln(1+sum_(n=1)^infty(b_nx^n)/(n!))

of the exponential transform

1+sum_(n=1)^infty(b_nx^n)/(n!)=exp(sum_(n=1)^infty(a_nx^n)/(n!))

which relate sequences a_1, a_2, ... and b_1, b_2, ....

See also

Exponential Transform

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References

Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, pp. 19-20, 1995.

Referenced on Wolfram|Alpha

Logarithmic Transform

Cite this as:

Weisstein, Eric W. "Logarithmic Transform." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogarithmicTransform.html

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