论文标题
序列的差分和积分计算
Differential and Integral Calculus of Sequence
论文作者
论文摘要
我们创建了微积分的序列版本。首先，我们定义等效性，一些基本操作，序列的差异和积分。然后，我们提出了身份函数，功能函数，指数函数，双曲线功能，三角函数的序列版本，并为其找到Maclaurin系列的序列版本。指数函数的序列版本涉及不同的系列，包括Grandi的系列。通过使用此框架，我们找到了二项式定理和Euler身份的序列版本。此外，我们设计了斐波那契序列及其概括的新形式主义。最后，我们提出了一个循序分子和钟数的序列偶，并找到有关素数（Wilson's Theorem）的模块化属性的序列双重属性和有关质量数的钟数。
We create a sequence version of calculus. First, we define equivalence, some fundamental operations, differential, and integral for sequences. Then, we propose sequence versions of identity function, power function, exponential function, hyperbolic function, trigonometric function, and also find sequence versions of the Maclaurin series for them. The sequence versions of exponential function involve divergent series including Grandi's series. By using this framework, we find a sequence version of the binomial theorem and Euler's identity. In addition, we design new formalisms of Fibonacci sequence and its generalizations. Last, we propose a sequence dual of factorial and Bell number, and find sequence dual of modular property of factorial concerning prime number (Wilson's theorem) and of Bell number concerning prime number.
