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convert/Cylinder

convert special functions admitting 1F1 or 0F1 hypergeometric representation into Cylinder functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

convert(expr, Cylinder)

Parameters

expr

-

Maple expression, equation, or set or list of them

Description

• 

convert/Cylinder converts, when possible, special functions admitting a 1F1 or 0F1 hypergeometric representation into Cylinder functions. The Cylinder functions are

FunctionAdvisor( Cylinder );

The 3 functions in the "Cylinder" class are:

CylinderD,CylinderU,CylinderV

(1)

Examples

HermiteHa,zLaguerreL1a2,12,1z22

HermiteHa,zLaguerreL12a,12,12z2

(2)

convert,Cylinder

12CylinderDa,z2ⅇ12z2binomial12+12a,12aⅇ14z2Γ1212aCylinderDa,zπ+12CylinderDa,z2ⅇ12z2binomial12+12a,12aⅇ14z2Γ1212aCylinderDa,zπ

(3)

erfca,z

erfca,z

(4)

convert,Cylinderassuminga::posint

CylinderDa1,z22ⅇ12z22aπ

(5)

2π12zhypergeom1a2+34,32,1z2221a214Γ1a2+14+π12hypergeom1a2+14,12,1z22Γ1a2+3421a234

2πzhypergeom12a+34,32,12z2212a14Γ12a+14+πhypergeom12a+14,12,12z2Γ12a+34212a34

(6)

convert,Cylinder

12ⅇ14z2212a+14212a14212a+34212a34CylinderD12a,z212a14212a34+12ⅇ14z2212a+14212a14+212a+34212a34CylinderD12a,z212a14212a34

(7)

collect,CylinderD,simplify

2ⅇ14z2CylinderD12a,z

(8)

When converting to a function class (e.g. Cylinder) it is possible to request additional conversion rules to be performed. Compare for instance these two different outputs:

MeijerG141a2,,0,12,1z22

MeijerG12a+14,,0,12,12z2

(9)

convert,Cylinder

12ⅇ14z2212a+34Γ12+aCylinderD12a,zπz2a12+12ⅇ14z2CylinderD12a,z212a+34Γ12+aπz2a12

(10)

convert,Cylinder,raise a

ⅇ14z2212a+34Γ12+aCylinderDa+12,z2a1π2a12+ⅇ14z2212a+34Γ12+aCylinderDa+12,z2a1π2a12ⅇ14z2212a+34Γ12+aCylinderDa+32,z2a1πz2a12+ⅇ14z2CylinderDa+32,z212a+34Γ12+a2a1πz2a12

(11)

See Also

convert

convert/to_special_function

FunctionAdvisor

 


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