Difference between revisions of "Sine integral"
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The sine integral is defined by | The sine integral is defined by | ||
$$\mathrm{Si}(z) = \displaystyle\int_0^z \mathrm{sinc}(t) \mathrm{d}t, \quad |\mathrm{arg} z|<\pi,$$ | $$\mathrm{Si}(z) = \displaystyle\int_0^z \mathrm{sinc}(t) \mathrm{d}t, \quad |\mathrm{arg} z|<\pi,$$ | ||
| − | where $\mathrm{sinc}$ denotes the [[ | + | where $\mathrm{sinc}$ denotes the [[sinc]] function. |
<div align="center"> | <div align="center"> | ||
Revision as of 00:19, 9 August 2016
The sine integral is defined by $$\mathrm{Si}(z) = \displaystyle\int_0^z \mathrm{sinc}(t) \mathrm{d}t, \quad |\mathrm{arg} z|<\pi,$$ where $\mathrm{sinc}$ denotes the sinc function.
Graph of $\mathrm{Si}$.
Domain coloring of $\mathrm{Si}$.
Properties
Relationship between exponential integral Ei, cosine integral, and sine integral
Videos
Laplace Transform of Sine Integral
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): 5.2.1
