7.41–7.42 Laguerre polynomials

7.411

1. 

0tLn(x)dx=Ln(t)Ln+1(t)/(n+1)

si558_e  MO 110

2. 

0tLnα(x)dx=Lnα(t)Ln+1α(t)(n+αn)+(n+1+αn+1)

si559_e  EH II 189(16)a

3. 

0tLn1α+1(x)dx=Lnα(t)+(n+αn)

si560_e  EH II 189(15)a

4. 

0tLm(x)Ln(t-x)dx=Lm+n(t)Lm+n+1(t)

si561_e  EH II 191(31)

5. 

k=0[0tLk(x)k!dx]2=et1[t0]

  MO 110

7.412

1. 

01(1x)μ1xαLnα(ax)dx=Γ(α+n+1)Γ(μ)Γ(α+μ+n+1)Lnα+μ(a)

  EH II 191(30)a, ...

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