convert/Cylinder - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Conversions : Function Class : convert/Cylinder

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,zLaguerreLa2,12,z22

(2)

convert,Cylinder

CylinderDa,z2ⅇz2212+a2a2ⅇz24Γ12a2CylinderDa,z2π+CylinderDa,z2ⅇz2212+a2a2ⅇz24Γ12a2CylinderDa,z2π

(3)

erfca,z

erfca,z

(4)

convert,Cylinderassuminga::posint

CylinderDa1,z22ⅇz222aπ

(5)

2Pi12zhypergeom1a2+34,32,1z2221a214GAMMA1a2+14+Pi12hypergeom1a2+14,12,1z22GAMMA1a2+3421a234

2πzhypergeoma2+34,32,z222a214Γa2+14+πhypergeoma2+14,12,z22Γa2+342a234

(6)

convert,Cylinder

ⅇz242a2+142a2142a2+342a234CylinderD12a,z22a2142a234+ⅇz242a2+142a214+2a2+342a234CylinderD12a,z22a2142a234

(7)

collect,CylinderD,simplify

2ⅇz24CylinderD12a,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

MeijerGa2+14,,0,12,z22

(9)

convert,Cylinder

ⅇz242a2+34Γa+12CylinderD12a,z2πz2a12+ⅇz24CylinderD12a,z2a2+34Γa+122πz2a12

(10)

convert,Cylinder,raise a

ⅇz242a2+34Γa+12CylinderDa+12,z2a1π2a12+ⅇz242a2+34Γa+12CylinderDa+12,z2a1π2a12ⅇz242a2+34Γa+12CylinderDa+32,z2a1πz2a12+ⅇz24CylinderDa+32,z2a2+34Γa+122a1πz2a12

(11)

See Also

convert

convert/to_special_function

FunctionAdvisor