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Convert to hypergeometric function


          How do you express the following function functions in terms of
the hypergeometric function ?

  ExponentialIntegral Ei(x)
  LogarithmicIntegral Li(x)

 Trigonometric functions:
  sin(x)               arcsin(x)
  cos(x)              arccos(x)
  tan(x)               arctan(x)
  cot(x)               arccot(x)
  sec(x)              arcsec(x)
 cosec(x)           arccosec(x)

 Similarly the hyperbolic functions  :  sinh(x) cosh(x) tanh(x) ;;;
arcsinh(x)  arccosh(x)  arctanh(x)

 The logarithmic function:    log(1+x) or log(x)
 the gamma function      :    gamma(n)
 the lambert function     :    lambertW(n,x)

  PLEASE provide the solutions for all the above cases (if possible)



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