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# Exponential Transform

The exponential transform is the transformation of a sequence , , ... into a sequence , , ... according to the equation

The inverse ("logarithmic") transform is then given by

The exponential transform relates the number of labeled connected graphs on nodes satisfying some property with the corresponding total number (not necessarily connected) of labeled graphs on nodes. In this application, the transform is called Riddell's formula for labeled graphs.

Binomial Transform, Euler Transform, Logarithmic Transform, Möbius Transform, Riddell's Formula, Stirling 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

Exponential Transform

## Cite this as:

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