In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its …

4 天之前 · Let E_1(x) be the En-function with n=1, E_1(x) = int_1^infty(e^(-tx)dt)/t (1) = int_x^infty(e^(-u)du)/u. (2) Then define the exponential integral Ei(x) by E_1(x)=-Ei(-x), (3) …

In the following formulas, erf is the error function and Ei is the exponential integral. ∫ e c x ln ⁡ x d x = 1 c ( e c x ln ⁡ | x | − Ei ⁡ ( c x ) ) {\displaystyle \int e^{cx}\ln x\,dx={\frac …

The previous integrals are all interrelated and are called exponential integrals. Instead of the above classical definitions through definite integrals, equivalent definitions through infinite …

2025年1月17日 · Integrals of Exponential Functions. The exponential function is perhaps the most efficient function in terms of the operations of calculus. The exponential function, \(y=e^x\), is …

The best-known properties and formulas for exponential integrals. Real values for real arguments. For real values of parameter and positive argument , the values of the exponential integral are …

The exponential function is perhaps the most efficient function in terms of the operations of calculus. The exponential function, [latex]y={e}^{x},[/latex] is its own derivative and its own …

2024年1月11日 · The integral exponential function can be represented by the series $$ \tag{1 } \mathop{\rm Ei} ( x) = \ c + \mathop{\rm ln} ( - x ) + \sum_{k=1}^ \infty \frac{x ^ {k} }{k!k} ,\ \ x < …

Integrals, Exponential Functions, and Logarithms. The earlier treatment of logarithms and exponential functions did not define the functions precisely and formally. This section develops …

The best-known properties and formulas for exponential integrals. For real values of parameter and positive argument , the values of the exponential integral are real (or infinity). For real …