DLMF:

19 Elliptic Integrals Legendre’s Integrals 19.3 Graphics 19.3 Graphics 19.4 Derivatives and Differential Equations

Figure 19.3.2 (See in context.)

Figure 19.3.2: $\mathop{R_{C}\/}\nolimits\!\left(x,1\right)$ and the Cauchy principal value of $\mathop{R_{C}\/}\nolimits\!\left(x,-1\right)$ for $0\leq x\leq 5$ . Both functions are asymptotic to $\mathop{\ln\/}\nolimits\!\left(4x\right)/\sqrt{4x}$ as $x\to\infty$ ; see (19.2.19) and (19.2.20). Note that $\mathop{R_{C}\/}\nolimits\!\left(x,\pm y\right)=y^{{-1/2}}\mathop{R_{C}\/}% \nolimits\!\left(x/y,\pm 1\right)$ ,

Annotations:

Symbols:: $\mathop{R_{C}\/}\nolimits\!\left(x,y\right)$ : Carlson’s combination of inverse circular and inverse hyperbolic functions and $\mathop{\ln\/}\nolimits z$ : principal branch of logarithm function
Permalink:: http://dlmf.nist.gov/19.3.F2.mag
Encodings:: Magnified png, pdf

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