code: def elliprc(ctx, x, y, pv=True):
      r"""
      Evaluates the degenerate Carlson symmetric elliptic integral
      of the first kind
  
      .. math ::
  
          R_C(x,y) = R_F(x,y,y) =
              \frac{1}{2} \int_0^{\infty} \frac{dt}{(t+y) \sqrt{(t+x)}}.
  
      If `y \in (-\infty,0)`, either a value defined by continuity,
      or with *pv=True* the Cauchy principal value, can be computed.
  
      If `x \ge 0, y > 0`, the value can be expressed in terms of
      elementary functions as
  
      .. math ::
  
          R_C(x,y) =
          \begin{cases}
            \dfrac{1}{\sqrt{y-x}}
              \cos^{-1}\left(\sqrt{\dfrac{x}{y}}\right),   & x < y \\
            \dfrac{1}{\sqrt{y}},                          & x = y \\
            \dfrac{1}{\sqrt{x-y}}
              \cosh^{-1}\left(\sqrt{\dfrac{x}{y}}\right),  & x > y \\
          \end{cases}.
  
      **Examples**
  
      Some special values and limits::
  
          >>> from mpmath import *
          >>> mp.dps = 25; mp.pretty = True
          >>> elliprc(1,2)*4; elliprc(0,1)*2; +pi
          3.141592653589793238462643
          3.141592653589793238462643
          3.141592653589793238462643
          >>> elliprc(1,0)
          +inf
          >>> elliprc(5,5)**2
          0.2
          >>> elliprc(1,inf); elliprc(inf,1); elliprc(inf,inf)
          0.0
          0.0
          0.0
  
      Comparing with the elementary closed-form solution::
  
          >>> elliprc('1/3', '1/5'); sqrt(7.5)*acosh(sqrt('5/3'))
          2.041630778983498390751238
          2.041630778983498390751238
          >>> elliprc('1/5', '1/3'); sqrt(7.5)*acos(sqrt('3/5'))
          1.875180765206547065111085
          1.875180765206547065111085
  
      Comparing with numerical integration::
  
          >>> q = extradps(25)(quad)
          >>> elliprc(2, -3, pv=True)
          0.3333969101113672670749334
          >>> elliprc(2, -3, pv=False)
          (0.3333969101113672670749334 + 0.7024814731040726393156375j)
          >>> 0.5*q(lambda t: 1/(sqrt(t+2)*(t-3)), [0,3-j,6,inf])
          (0.3333969101113672670749334 + 0.7024814731040726393156375j)
  
      """
      x = ctx.convert(x)
      y = ctx.convert(y)
      prec = ctx.prec
      try:
          ctx.prec += 20
          tol = ctx.eps * 2**10
          v = RC_calc(ctx, x, y, tol, pv)
      finally:
          ctx.prec = prec
      return +v
  
imports: from .functions import defun, defun_wrapped
label_desc: Use image node_id 14 for calling a global function with example usage: elliprc(ctx, x, y, pv) and returns: unknown