Lamé Functions - 29.3 Definitions and Basic Properties

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29.3#Ex3 α p = 1 2 ⁢ ( ν - 2 ⁢ p - 2 ) ⁢ ( ν + 2 ⁢ p + 3 ) ⁢ k 2 subscript 𝛼 𝑝 1 2 𝜈 2 𝑝 2 𝜈 2 𝑝 3 superscript 𝑘 2 {\displaystyle{\displaystyle\alpha_{p}=\tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}}}
\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}		 

alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)*(k)^(2)
 
Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)*(k)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex4 γ p = 1 2 ⁢ ( ν - 2 ⁢ p + 1 ) ⁢ ( ν + 2 ⁢ p ) ⁢ k 2 subscript 𝛾 𝑝 1 2 𝜈 2 𝑝 1 𝜈 2 𝑝 superscript 𝑘 2 {\displaystyle{\displaystyle\gamma_{p}=\tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}}}
\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}		 

((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)*(k)^(2)
 
(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)*(k)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex5 α p = 1 2 ⁢ ( ν - 2 ⁢ p - 2 ) ⁢ ( ν + 2 ⁢ p + 3 ) ⁢ k 2 subscript 𝛼 𝑝 1 2 𝜈 2 𝑝 2 𝜈 2 𝑝 3 superscript 𝑘 2 {\displaystyle{\displaystyle\alpha_{p}=\tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}}}
\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}		 

alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)*(k)^(2)
 
Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)*(k)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex6 γ p = 1 2 ⁢ ( ν - 2 ⁢ p + 1 ) ⁢ ( ν + 2 ⁢ p ) ⁢ k 2 subscript 𝛾 𝑝 1 2 𝜈 2 𝑝 1 𝜈 2 𝑝 superscript 𝑘 2 {\displaystyle{\displaystyle\gamma_{p}=\tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}}}
\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}		 

((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)*(k)^(2)
 
(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)*(k)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex7 α p = 1 2 ⁢ ( ν - 2 ⁢ p - 3 ) ⁢ ( ν + 2 ⁢ p + 4 ) ⁢ k 2 subscript 𝛼 𝑝 1 2 𝜈 2 𝑝 3 𝜈 2 𝑝 4 superscript 𝑘 2 {\displaystyle{\displaystyle\alpha_{p}=\tfrac{1}{2}(\nu-2p-3)(\nu+2p+4)k^{2}}}
\alpha_{p} = \tfrac{1}{2}(\nu-2p-3)(\nu+2p+4)k^{2}		 

alpha[p] = (1)/(2)*(nu - 2*p - 3)*(nu + 2*p + 4)*(k)^(2)
 
Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 3)*(\[Nu]+ 2*p + 4)*(k)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex8 β p = ( 2 ⁢ p + 2 ) 2 ⁢ ( 2 - k 2 ) subscript 𝛽 𝑝 superscript 2 𝑝 2 2 2 superscript 𝑘 2 {\displaystyle{\displaystyle\beta_{p}=(2p+2)^{2}(2-k^{2})}}
\beta_{p} = (2p+2)^{2}(2-k^{2})		 

beta[p] = (2*p + 2)^(2)*(2 - (k)^(2))
 
Subscript[\[Beta], p] == (2*p + 2)^(2)*(2 - (k)^(2))
 Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex9 γ p = 1 2 ⁢ ( ν - 2 ⁢ p ) ⁢ ( ν + 2 ⁢ p + 1 ) ⁢ k 2 subscript 𝛾 𝑝 1 2 𝜈 2 𝑝 𝜈 2 𝑝 1 superscript 𝑘 2 {\displaystyle{\displaystyle\gamma_{p}=\tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}}}
\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}		 

((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)*(k)^(2)
 
(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)*(k)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
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