Special Functions (B.Sc notes)
19 videos • 85 views • by Doctor of Mathematics
Special Functions (B.Sc notes)
1
Prove that J3+3J'0+4J'''=0
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2
Hazrat Muhammad صلى الله عليه وسلم Ka Bachpan - Part 2 - Sayyad Aminul Qadri
Shemaroo Ibaadat
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3
A solution of the differential equation 2x^2.d^2y/dx^2+3xdy/dx-y=0,x 0 that passes through the (1,1)
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4
Explanation of Shab-e-miraj and Isra on basis on special theory of relativity
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5
Prove that: integrate -1 to+1 (1-x^2) (P'n) ^2dx=2n(n+1)/(2n+1)
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6
Integral e^-ax.J(bx) from x=0 to x=infinity =1/√a^2+b^2
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7
prove that L-1{8/(p^2+1)^3}=(3-t^2)sint-3tcost
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8
Find Fourier sine transform of f(x), if:f(x)=0 if x between 0 and a, x if a and b, 0 if greater b
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9
Find Fourier cosine transform of f(x)=1/(1+x^2) hence find Fourier sine transform of F(x)=x/(1+x^2)
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10
Find: L-1{p/(p^4+p^2+1)}
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11
Integrate from -1 to +1 ∫Pm(x). Pn(x) dx=0 (orthogonal property of Legendre's Polynomial)
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12
Solve by Laplace transform (D+1)^2=t, y=-3 when t=0 and y=-1, when t=1.
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13
f(x)=10x^3-3x^2-5x-1 in terms of Legendre's polynomial.Write Legendre's functions Pn(x) and Qn(x)
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14
∫e^-ax.P(b√x)dx=1/a.e^-b^2/4a from x=0 to x=♾️. Bessel Function Special Function|Important Example
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15
Prove that Jn(x)=1/π∫cos(nθ-xsinθ)dθ,n=0,1,2,....(Integral Representation of Bessel Function)
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16
(i) ∫sinax.J0(bx)dx=0,if b a,1/√(a^2+b^2),if b a,(ii) ∫cosax.J0(bx)dx=1/√(b^2-a^2),if b a,0 if b a.
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17
Pn(cosθ)=1.3.5...(2n-1)/2^n.n!.2cosnθ+1/2.1.3.5...(2n-3)/2^n-1.n-1!.2cos(n-2)θ+1.3/2.4.1.3.5...(2n-)
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18
Prove that J'0=-J1
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19
Prove that J2-J0=2J"0
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