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21: 1.14 Integral Transforms

… ►If also ${lim}_{t\to 0+}f(t)/t$ exists, then … ►where $A_p=\tan \left(\frac{1}{2}\pi /p\right)$ when , or $\cot \left(\frac{1}{2}\pi /p\right)$ when $p\ge 2$. … ►If the integral converges, then it converges uniformly in any compact domain in the complex $s$-plane not containing any point of the interval $(-\mathrm{\infty },0]$. … ►

Table 1.14.3: Fourier sine transforms.

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$f(t)$	$\sqrt{{\displaystyle \frac{2}{\pi }}}{\displaystyle {\int }_0^{\mathrm{\infty }}}f(t)\sin \left(xt\right)dt$,	$x>0$
…
$t^{-1/2}$	$x^{-1/2}$
$t^{-3/2}$	$2x^{1/2}$
…

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22: Bibliography K

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A Program for Computing the Conical Functions of the First Kind $P_{-1/2+i\tau }^m(x)$ for $m=0$ and $m=1$ . Comput. Phys. Comm. 23 (1), pp. 51–61.

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Notes:

Single-precision Fortran, maximum accuracy 15D.

External Links:

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Referenced by:

§14.31(ii), 1st item.

Encodings:

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… ►

Compact quantum groups and $q$-special functions. In Representations of Lie Groups and Quantum Groups, Pitman Res. Notes Math. Ser., Vol. 311, pp. 46–128.

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Notes:

Sections 3 and 4 also available as arXiv:math/9403216

External Links:

MathReview (Eric M. Opdam)

Referenced by:

(18.27.14_3).

Encodings:

BibTeX

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