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{Si}(z) = \displaystyle\int_0^z \mathrm{sinc}(t) \mathrm{d}t, \quad |\mathrm{arg} \hspace{2pt} z|<\pi,$$ |
| − | where $\mathrm{sinc}$ denotes the [[ | + | where $\mathrm{sinc}$ denotes the [[sinc]] function. |
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File: | + | File:Siplot.png| Graph of $\mathrm{Si}$. |
| − | File: | + | File:Complexsiplot.png|[[Domain coloring]] of $\mathrm{Si}$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
| + | |||
| + | =Properties= | ||
| + | [[Derivative of sine integral]]<br /> | ||
| + | [[Antiderivative of sine integral]]<br /> | ||
| + | [[Relationship between exponential integral Ei, cosine integral, and sine integral]]<br /> | ||
=Videos= | =Videos= | ||
| − | [https://www.youtube.com/watch?v=hMW7aIYoN7U Laplace Transform of Sine Integral] | + | [https://www.youtube.com/watch?v=hMW7aIYoN7U Laplace Transform of Sine Integral (2 January 2015)] |
=References= | =References= | ||
| − | * | + | * {{BookReference|Special Functions of Mathematical Physics and Chemistry|1956|Ian N. Sneddon|prev=Cosine integral|next=Error function}}: $\S 5 (5.10)$ |
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=}}: $5.2.1$ | ||
| + | |||
| + | {{:*-integral functions footer}} | ||
| − | + | [[Category:SpecialFunction]] | |
Latest revision as of 00:42, 25 June 2017
The sine integral is defined by $$\mathrm{Si}(z) = \displaystyle\int_0^z \mathrm{sinc}(t) \mathrm{d}t, \quad |\mathrm{arg} \hspace{2pt} z|<\pi,$$ where $\mathrm{sinc}$ denotes the sinc function.
Graph of $\mathrm{Si}$.
Domain coloring of $\mathrm{Si}$.
Properties
Derivative of sine integral
Antiderivative of sine integral
Relationship between exponential integral Ei, cosine integral, and sine integral
Videos
Laplace Transform of Sine Integral (2 January 2015)
References
- 1956: Ian N. Sneddon: Special Functions of Mathematical Physics and Chemistry ... (previous) ... (next): $\S 5 (5.10)$
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): $5.2.1$
