# Recurrence relation of exponential integral E

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## Theorem

The following formula holds for $n=1,2,3,\ldots$: $$E_{n+1}(z)=\dfrac{e^{-z}-zE_n(z)}{n},$$ where $E_n$ denotes the exponential integral E.

## Proof

## References

- 1964: Milton Abramowitz and Irene A. Stegun:
*Handbook of mathematical functions*... (previous) ... (next): $5.1.14$