The Kummer M_{mu,nu}(z) function - Maple Help

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KummerM - The Kummer M_{mu,nu}(z) function

KummerU - The Kummer U_{mu,nu}(z) function

Calling Sequence

KummerM(mu, nu, z)

KummerU(mu, nu, z)

Parameters

mu

-

algebraic expression

nu

-

algebraic expression

z

-

algebraic expression

Description

• 

The Kummer functions KummerM(mu, nu, z) and KummerU(mu, nu, z) solve the differential equation

zy''+nuzy'muy=0

Examples

KummerM1,2,0.5

1.297442541

(1)

evalfKummerU12,13,17

0.9025082951

(2)

zKummerMμ,ν,z

z+μνKummerMμ,ν,z+νμKummerM1+μ,ν,zz

(3)

seriesKummerU12,13,z,z

3Γ56Γ23ππ3z2/3Γ23+92Γ56Γ23zπ710π3z5/3Γ23+8132Γ56Γ23z2π91320π3z8/3Γ23+405448Γ56Γ23z3π172921120π3z11/3Γ23+2431024Γ56Γ23z4π123567584π3z14/3Γ23+6561133120Γ56Γ23z5π76572297856π3z17/3Γ23+Oz6

(4)

See Also

hypergeom, inifcns, Whittaker

References

  

Abramowitz, M., and Stegun, I., eds. Handbook of Mathematical Functions. New York: Dover, 1972.


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