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Schlömilch's Function


$\displaystyle S(\nu,z)$ $\textstyle \equiv$ $\displaystyle \int_0^\infty (1+t)^{-\nu} e^{-zt}\,dt = z^{\nu-1} e^z\int_z^\infty u^{-\nu} e^{-u}\,du$  
  $\textstyle =$ $\displaystyle z^{\nu/2-1}e^{z/2} W_{-\nu/2,(1-\nu)/2}(z),$  

where $W_{k,m}(z)$ is the Whittaker Function.




© 1996-9 Eric W. Weisstein
1999-05-26