4. (25 points) Find the value of J-5/2(x) using the properties of Bessel Functions. d_[xJ, (x)]...

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4. (25 points) Find the value of J-5/2(x) using the properties of Bessel Functions. d_[x²J, (x)] = x²J₁_, (x) d_[x-*J₁ (x)] = -x ²" J₁+₁(x) v+1 a. b. C. J₁ (x) = — (J₂_₁ (x) + J ₁+₁ (x)) 2v d. J,₁'(x) = — (J ₁₁ (x) - J , (x)) 2 e. J₁'(x) = — J₁, (x) - J₁+1 (X) X f. J ₂₁ (x) = ²¹ J, (x) — J₁_, (x) 4. (25 points) Find the value of J-5/2(x) using the properties of Bessel Functions. d_[x²J, (x)] = x²J₁_, (x) d_[x-*J₁ (x)] = -x ²" J₁+₁(x) v+1 a. b. C. J₁ (x) = — (J₂_₁ (x) + J ₁+₁ (x)) 2v d. J,₁'(x) = — (J ₁₁ (x) - J , (x)) 2 e. J₁'(x) = — J₁, (x) - J₁+1 (X) X f. J ₂₁ (x) = ²¹ J, (x) — J₁_, (x)