SHI Hyperbolic Sine Integral
SHI.1 Introduction |
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Let
be a complex variable of
.The function Hyperbolic Sine Integral (noted
) is defined by the following third order differential equation
| SHI.1.1 |
Although
is a singularity of SHI.1.1, the initial conditions can be given by
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SHI.1.2 |
Related function: Hyperbolic Cosine Integral
SHI.2 Series and asymptotic expansions |
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SHI.2.1 Asymptotic expansion at
|
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SHI.2.1.2 General form |
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SHI.2.1.2.2 Auxiliary function
The coefficients
![$u (n)$](SHI_16.gif)
![$y _{1} (x)$](SHI_17.gif)
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SHI.2.1.2.3 Auxiliary function
The coefficients
![$u (n)$](SHI_22.gif)
![$y _{2} (x)$](SHI_23.gif)
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SHI.2.2 Asymptotic expansion at
|
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SHI.2.2.2 General form |
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| SHI.2.2.2.1 |
![$u (n)$](SHI_30.gif)
| SHI.2.2.2.2 |
| SHI.2.2.2.3 |
| SHI.2.2.2.4 |