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KummerM

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

KummerU

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

 

Calling Sequence

Parameters

Description

Examples

References

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

3Γ56Γ23ππ3z23Γ23+9Γ56Γ23z2π7π3z5310Γ23+81Γ56Γ23z232π91π3z83320Γ23+405Γ56Γ23z3448π1729π3z11321120Γ23+243Γ56Γ23z41024π1235π3z14367584Γ23+6561Γ56Γ23z5133120π7657π3z1732297856Γ23+Oz6

(4)

References

  

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

See Also

hypergeom

inifcns

Whittaker