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convert/1F1 - convert to special functions admitting a 1F1 hypergeometric representation
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Calling Sequence
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convert(expr, `1F1`)
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Parameters
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expr
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a Maple expression, equation, or a set or list of them.
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Description
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convert/1F1 converts, when possible, hypergeometric, MeijerG, and special functions admitting a 0F1 hypergeometric representation into special functions admitting a 1F1 hypergeometric representation; that is, into one of
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FunctionAdvisor( `1F1` );
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The 20 functions in the "1F1" class are particular cases of the hypergeometric function and are given by:
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![[CoulombF, CylinderD, CylinderU, CylinderV, Ei, FresnelC, FresnelS, Fresnelf, Fresnelg, GAMMA, HermiteH, KummerM, KummerU, LaguerreL, WhittakerM, WhittakerW, dawson, erf, erfc, erfi]](/support/helpjp/helpview.aspx?si=7045/file03627/math46.png)
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Examples
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![hypergeom([], [c], z)](/support/helpjp/helpview.aspx?si=7045/file03627/math74.png)
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![hypergeom([], [c], z)](/support/helpjp/helpview.aspx?si=7045/file03627/math77.png)
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![convert(hypergeom([], [c], z), `1F1`)](/support/helpjp/helpview.aspx?si=7045/file03627/math81.png)
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![MeijerG([[], []], [[(1/2)*a, -(1/2)*a], []], (1/4)*z^2)](/support/helpjp/helpview.aspx?si=7045/file03627/math88.png)
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![MeijerG([[], []], [[(1/2)*a, -(1/2)*a], []], (1/4)*z^2)](/support/helpjp/helpview.aspx?si=7045/file03627/math91.png)
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![convert(MeijerG([[], []], [[(1/2)*a, -(1/2)*a], []], (1/4)*z^2), `1F1`)](/support/helpjp/helpview.aspx?si=7045/file03627/math95.png)
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