convert functions in an expression to hypergeometric form - Maple Help

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convert/hypergeom - convert functions in an expression to hypergeometric form

Calling Sequence

convert( expr, hypergeom, opt_1, opt_2, ... )

Parameters

expr

-

expression

opt_i

-

optional arguments, see convert/to_special_function

Description

• 

Converts the functions found in expr, including sum and Sum, to their hypergeometric forms when possible. For sums, no attempt is made to ensure that the resulting hypergeometric function is convergent or terminates.

Examples

k=1∞1kbinomialk+n,k

k=1∞1kbinomialk+n,k

(1)

convert,hypergeom

1n

(2)

BesselJa,z

BesselJa,z

(3)

=convert,hypergeom

BesselJa,z=zahypergeom,1+a,14z2Γ1+a2a

(4)

LegendrePa,b,z

LegendrePa,b,z

(5)

=convert,hypergeom

LegendrePa,b,z=z+112bhypergeoma,1+a,1b,1212zz112bΓ1b

(6)

KummerUa,b,z

KummerUa,b,z

(7)

=convert,hypergeom

KummerUa,b,z=Γ1+bhypergeomab+1,2b,zz1+bΓa+Γ1bhypergeoma,b,zΓab+1

(8)

For negative a we have

=convert,hypergeomassuminga::negint

KummerUa,b,z=pochhammerab+1,ahypergeoma,b,z

(9)

Elementary functions are not converted by default (see convert/to_special_function)

convertsinz,hypergeom

sinz

(10)

To convert them use either of the optional arguments: include=elementary, or include=all

sinz

sinz

(11)

=convert,hypergeom,include=all

sinz=zhypergeom,32,14z2

(12)

See Also

convert, convert/MeijerG, convert/to_special_function, hypergeom, simplify/hypergeom


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