6.52 Bessel functions combined with x and x2

6.521

1. 

0xJν(ax)Jν(βx)dx=βJν1(β)Jν(α)αJν1(α)Jν(β)α2β2[αβ,ν>1]=αJν1(β)Jν(α)βJν(α)Jν(β)β2α2[αβ,ν>1]

si519_e  WH

2.10 

0xKv(ax)Jv(bx)dx=bvav(b2+a2)[Rea>0,b>0,Rev>1]

si520_e  ET II 63(2)

3. 

0xKv(ax)Kv(bx)dx=π(ab)v(a2vb2v)2sin(vπ)(a2b2)[|Rev|>1,Re(a+b)>0]

si521_e  ET II 45(48)

4. 

0xJv(λx)Kv(μx)dx=(μ2+λ2)1[(λμ)v+λaJv+1(λa)Kv(μa)μaJv(λa)Kv+1(μa)]

  ET II 367(26)

[Reν>1]

5. 

0xK1(ax)=π2a2[

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