## Divergence Series and Integrals From the Viewpoint of the Division by Zero Calculus

**Authors:** Saburou Saitoh

In this short note, we would like to refer to the fundamental new interpretations that for the fundamental expansion $1/(1-z) = \sum_{j=0}^{\infty} z^j$ it is valid in the sense $0=0$ for $z=1$, for the integral $\int_1^{\infty} 1/x dx $ it is zero and in the formula $\int_0^{\infty} J_0(\lambda t) dt = 1/\lambda$, it is valid with $0=0$ for $\lambda =0$ in the sense of the division by zero.

**Comments:** 8 Pages. In this short note, we would like to refer to the fundamental new interpretations that for the fundamental expansion $1/(1-z) = \sum_{j=0}^{\infty} z^j$ it is valid in the sense $0=0$ for $z=1$, for the integral $\int_1^{\infty} 1/x dx $ it is zero and i

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### Submission history

[v1] 2019-10-21 19:54:08

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