gam%C3%A9%E2%80%93Wangerin%20functions

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1: 18.42 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … ►A more complete list of available software for computing these functions, and for generating formulas symbolically, is found in the Software Index. For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C3). …

2: 22.22 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … ►For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C13). …

3: 23.24 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … ►A more complete list of available software for computing these functions is found in the Software Index. For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C15). … ►No research software has been found for these functions. …

4: 16.27 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … ►A more complete list of available software for computing these functions is found in the Software Index. For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C19). …

5: 28.36 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … ►A more complete list of available software for computing these functions is found in the Software Index. For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C17). … ►

§28.36(iii) Mathieu and Modified Mathieu Functions

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6: 33.26 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … ►A more complete list of available software for computing these functions is found in the Software Index. For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C12). …

7: 11.16 Software

… ►For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C10e). ►

§11.16(ii) Struve Functions

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§11.16(iii) Integrals of Struve Functions

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§11.16(iv) Lommel Functions

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§11.16(v) Anger and Weber Functions

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8: 4.48 Software

… ►All scientific programming languages, libraries, and systems support computation of at least some of the elementary functions in standard floating-point arithmetic (§3.1(i)). … ►Links to research literature for the Lambert $W$-function and for test software are included also. … ►A more complete list of available software for computing these functions is found in the Software Index; again, software that uses only standard floating-point arithmetic is excluded. For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C4). … ►

§4.48(iv) Lambert $W$-Function

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9: 13.32 Software

… ►In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … ►A more complete list of available software for computing these functions is found in the Software Index. For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C11). …

10: 9.1 Special Notation

… ►(For other notation see Notation for the Special Functions.) ► ►►

$k$	nonnegative integer, except in §9.9(iii).
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►The main functions treated in this chapter are the Airy functions $\mathrm{Ai}\left(z\right)$ and $\mathrm{Bi}\left(z\right)$, and the Scorer functions $\mathrm{Gi}(z)$ and $\mathrm{Hi}(z)$ (also known as inhomogeneous Airy functions). ►Other notations that have been used are as follows: $\mathrm{Ai}\left(-x\right)$ and $\mathrm{Bi}\left(-x\right)$ for $\mathrm{Ai}\left(x\right)$ and $\mathrm{Bi}\left(x\right)$ (Jeffreys (1928), later changed to $\mathrm{Ai}\left(x\right)$ and $\mathrm{Bi}\left(x\right)$); $U(x)=\sqrt{\pi }\mathrm{Bi}\left(x\right)$, $V(x)=\sqrt{\pi }\mathrm{Ai}\left(x\right)$ (Fock (1945)); $A(x)=3^{-1/3}\pi \mathrm{Ai}\left(-3^{-1/3}x\right)$ (Szegő (1967, §1.81)); $e_0(x)=\pi \mathrm{Hi}(-x)$, ${\tilde{e}}_0(x)=-\pi \mathrm{Gi}(-x)$ (Tumarkin (1959)).