TOPICS
Search

Kummer's Series Transformation

Let sum_(k=0)^(infty)a_k=a and sum_(k=0)^(infty)c_k=c be convergent series such that

lim_(k->infty)(a_k)/(c_k)=lambda!=0.

Then

a=lambdac+sum_(k=0)^infty(1-lambda(c_k)/(a_k))a_k.

Explore with Wolfram|Alpha

References

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 16, 1972.

Referenced on Wolfram|Alpha

Kummer's Series Transformation

Cite this as:

Weisstein, Eric W. "Kummer's Series Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KummersSeriesTransformation.html

Subject classifications