Integral representations and integral transforms of some families of ...
Integral representations and integral transforms of some families of ...
Integral representations and integral transforms of some families of ...
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<strong>Integral</strong> Transforms <strong>and</strong> Special Functions 9<br />
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<strong>and</strong> [6, Vol. II, p. 37, Entry 8.7 (32)]<br />
∫ ∞<br />
√<br />
πb<br />
t −λ−1/2 J μ (at) cos(bt)dt =<br />
0<br />
2 · a μ Ɣ [1/2 (μ − λ + 1/2)]<br />
2 λ b μ−λ+1 Ɣ(μ + 1)Ɣ [1/2 (λ − μ + 1/2)]<br />
[ ( 1<br />
· 2F 1 μ − λ + 1 )<br />
, 1 (<br />
μ − λ + 3 ) ]<br />
; μ + 1; a2<br />
2 2 2 2 b 2<br />
( (<br />
R μ + 1 )<br />
)<br />
> R(λ) > −1; 0