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Erdős problem 270

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For integers a≥1a\geq1 and b≥1−ab\geq1-a, the series Ca,b=∑n=1∞n!/((a+1)n+b)!C_{a,b}=\sum_{n=1}^{\infty} n!/((a+1)n+b)! is transcendental. Equivalently, the series in Erdős Problem 270 is transcendental whenever f(n)=an+bf(n)=an+b is a positive integer-valued affine function.

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For integers $a\geq1$ and $b\geq1-a$, the series $C_{a,b}=\sum_{n=1}^{\infty} n!/((a+1)n+b)!$ is transcendental. Equivalently, the series in Erdős Problem 270 is transcendental whenever $f(n)=an+b$ is a positive integer-valued affine function.

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