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convert/2F1 - convert to special functions admitting a 2F1 hypergeometric representation
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Calling Sequence
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convert(expr, `2F1`)
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Parameters
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expr
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Maple expression, equation, or a set or list of them
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Description
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convert/2F1 converts, when possible, hypergeometric / MeijerG functions into special functions admitting a 2F1 hypergeometric representation; that is, into one of
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FunctionAdvisor( `2F1` );
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The 26 functions in the "2F1" class are particular cases of the hypergeometric function and are given by:
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![[ChebyshevT, ChebyshevU, EllipticCE, EllipticCK, EllipticE, EllipticK, GaussAGM, GegenbauerC, JacobiP, LegendreP, LegendreQ, LerchPhi, SphericalY, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, ln]](/support/helpjp/helpview.aspx?si=7044/file03628/math46.png)
| (1) |
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Examples
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![z*hypergeom([1/2, 1], [3/2], z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math60.png)
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![z*hypergeom([1/2, 1], [3/2], z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math63.png)
| (2) |
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![convert(z*hypergeom([1/2, 1], [3/2], z^2), `2F1`)](/support/helpjp/helpview.aspx?si=7044/file03628/math67.png)
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![hypergeom([-1/2, 1/2], [1], z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math74.png)
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![hypergeom([-1/2, 1/2], [1], z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math77.png)
| (4) |
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![convert(hypergeom([-1/2, 1/2], [1], z^2), `2F1`)](/support/helpjp/helpview.aspx?si=7044/file03628/math81.png)
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| (5) |
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![hypergeom([(1/2)*a+(1/2)*b+1/2, 1+(1/2)*a+(1/2)*b], [a+3/2], 1/z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math88.png)
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![hypergeom([1+(1/2)*a+(1/2)*b, (1/2)*a+(1/2)*b+1/2], [a+3/2], 1/z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math91.png)
| (6) |
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![convert(hypergeom([1+(1/2)*a+(1/2)*b, (1/2)*a+(1/2)*b+1/2], [a+3/2], 1/z^2), `2F1`)](/support/helpjp/helpview.aspx?si=7044/file03628/math95.png)
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| (7) |
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![hypergeom([b+c+a+1, -a], [1+b], 1/2-(1/2)*z)](/support/helpjp/helpview.aspx?si=7044/file03628/math102.png)
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![hypergeom([-a, b+c+a+1], [1+b], 1/2-(1/2)*z)](/support/helpjp/helpview.aspx?si=7044/file03628/math105.png)
| (8) |
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![convert(hypergeom([-a, b+c+a+1], [1+b], 1/2-(1/2)*z), `2F1`)](/support/helpjp/helpview.aspx?si=7044/file03628/math109.png)
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| (9) |
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![MeijerG([[0, 1/2], []], [[0], [-1/2]], -1/z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math116.png)
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![MeijerG([[0, 1/2], []], [[0], [-1/2]], -1/z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math119.png)
| (10) |
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![convert(MeijerG([[0, 1/2], []], [[0], [-1/2]], -1/z^2), `2F1`)](/support/helpjp/helpview.aspx?si=7044/file03628/math123.png)
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| (11) |
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![MeijerG([[1/2, 1/2], []], [[0], [0]], -1+z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math130.png)
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![MeijerG([[1/2, 1/2], []], [[0], [0]], -1+z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math133.png)
| (12) |
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![convert(MeijerG([[1/2, 1/2], []], [[0], [0]], -1+z^2), `2F1`)](/support/helpjp/helpview.aspx?si=7044/file03628/math137.png)
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| (13) |
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![MeijerG([[-(1/2)*a-(1/2)*b, 1/2-(1/2)*a-(1/2)*b], []], [[0], [-1/2-a]], -1/z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math144.png)
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![MeijerG([[-(1/2)*a-(1/2)*b, 1/2-(1/2)*a-(1/2)*b], []], [[0], [-a-1/2]], -1/z^2)](/support/helpjp/helpview.aspx?si=7044/file03628/math147.png)
| (14) |
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![convert(MeijerG([[-(1/2)*a-(1/2)*b, 1/2-(1/2)*a-(1/2)*b], []], [[0], [-1/2-a]], -1/z^2), `2F1`)](/support/helpjp/helpview.aspx?si=7044/file03628/math151.png)
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| (15) |
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![MeijerG([[-a, a+1], []], [[0], [b]], -1/2+(1/2)*z)](/support/helpjp/helpview.aspx?si=7044/file03628/math158.png)
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![MeijerG([[-a, a+1], []], [[0], [b]], -1/2+(1/2)*z)](/support/helpjp/helpview.aspx?si=7044/file03628/math161.png)
| (16) |
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![convert(MeijerG([[-a, a+1], []], [[0], [b]], -1/2+(1/2)*z), `2F1`)](/support/helpjp/helpview.aspx?si=7044/file03628/math165.png)
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| (17) |
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