Cricetine-Like Rodents from the Sespe Eocene of California.

نویسنده

  • R W Wilson
چکیده

11 IJ (zx)xe+l exp [1/2t(1 -x2)] dx = E t" z-'-' J +x÷i (z). ,./ n~~~~~~~-O In the first two expressions the Bessel functions of the first kind (J,'s) may be replaced throughout by functions of the second kind (Y,'s); and further, if the factor (-)" in the summation involving J,,-x(z) be omitted the functions of the first kind may be replaced throughout by modified functions of the second kind (K,'s). These equations, which hold for R(v), R(p) > 0, may be verified by replacing z dn u by VZ2 -z2k2skn2u, expanding the Bessel functions in the integrand, using Lommel's expansion, and integrating termwise. The last two equations, which hold when R(js) > -1 and which may be verified by using" zn+1 1l J^+n+)= fX!J (ZX)XI+l (1 -X2)xdx,

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عنوان ژورنال:
  • Proceedings of the National Academy of Sciences of the United States of America

دوره 21 1  شماره 

صفحات  -

تاریخ انتشار 2005