Heun Functions - 31.11 Expansions in Series of Hypergeometric Functions

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
31.11.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L_{0}c_{0}+M_{0}c_{1} = 0}
L_{0}c_{0}+M_{0}c_{1} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
L[0]*c[0]+ M[0]*c[1] = 0
 
Subscript[L, 0]*Subscript[c, 0]+ Subscript[M, 0]*Subscript[c, 1] == 0
 Skipped - no semantic math Skipped - no semantic math - -
31.11.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle K_{j}c_{j-1}+L_{j}c_{j}+M_{j}c_{j+1} = 0}
K_{j}c_{j-1}+L_{j}c_{j}+M_{j}c_{j+1} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
K[j]*c[j - 1]+ L[j]*c[j]+ M[j]*c[j + 1] = 0
 
Subscript[K, j]*Subscript[c, j - 1]+ Subscript[L, j]*Subscript[c, j]+ Subscript[M, j]*Subscript[c, j + 1] == 0
 Skipped - no semantic math Skipped - no semantic math - -
31.11.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle K_{j} = -\frac{(j+\alpha-\mu-1)(j+\beta-\mu-1)(j+\gamma-\mu-1)(j+\lambda-1)}{(2j+\lambda-\mu-1)(2j+\lambda-\mu-2)}}
K_{j} = -\frac{(j+\alpha-\mu-1)(j+\beta-\mu-1)(j+\gamma-\mu-1)(j+\lambda-1)}{(2j+\lambda-\mu-1)(2j+\lambda-\mu-2)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
K[j] = -((j + alpha - mu - 1)*(j + beta - mu - 1)*(j + gamma - mu - 1)*(j + lambda - 1))/((2*j + lambda - mu - 1)*(2*j + lambda - mu - 2))
 
Subscript[K, j] == -Divide[(j + \[Alpha]- \[Mu]- 1)*(j + \[Beta]- \[Mu]- 1)*(j + \[Gamma]- \[Mu]- 1)*(j + \[Lambda]- 1),(2*j + \[Lambda]- \[Mu]- 1)*(2*j + \[Lambda]- \[Mu]- 2)]
 Skipped - no semantic math Skipped - no semantic math - -
31.11.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L_{j} = a(\lambda+j)(\mu-j)-q+\frac{(j+\alpha-\mu)(j+\beta-\mu)(j+\gamma-\mu)(j+\lambda)}{(2j+\lambda-\mu)(2j+\lambda-\mu+1)}+\frac{(j-\alpha+\lambda)(j-\beta+\lambda)(j-\gamma+\lambda)(j-\mu)}{(2j+\lambda-\mu)(2j+\lambda-\mu-1)}}
L_{j} = a(\lambda+j)(\mu-j)-q+\frac{(j+\alpha-\mu)(j+\beta-\mu)(j+\gamma-\mu)(j+\lambda)}{(2j+\lambda-\mu)(2j+\lambda-\mu+1)}+\frac{(j-\alpha+\lambda)(j-\beta+\lambda)(j-\gamma+\lambda)(j-\mu)}{(2j+\lambda-\mu)(2j+\lambda-\mu-1)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
L[j] = a*(lambda + j)*(mu - j)- q +((j + alpha - mu)*(j + beta - mu)*(j + gamma - mu)*(j + lambda))/((2*j + lambda - mu)*(2*j + lambda - mu + 1))+((j - alpha + lambda)*(j - beta + lambda)*(j - gamma + lambda)*(j - mu))/((2*j + lambda - mu)*(2*j + lambda - mu - 1))
 
Subscript[L, j] == a*(\[Lambda]+ j)*(\[Mu]- j)- q +Divide[(j + \[Alpha]- \[Mu])*(j + \[Beta]- \[Mu])*(j + \[Gamma]- \[Mu])*(j + \[Lambda]),(2*j + \[Lambda]- \[Mu])*(2*j + \[Lambda]- \[Mu]+ 1)]+Divide[(j - \[Alpha]+ \[Lambda])*(j - \[Beta]+ \[Lambda])*(j - \[Gamma]+ \[Lambda])*(j - \[Mu]),(2*j + \[Lambda]- \[Mu])*(2*j + \[Lambda]- \[Mu]- 1)]
 Skipped - no semantic math Skipped - no semantic math - -
31.11.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M_{j} = -\frac{(j-\alpha+\lambda+1)(j-\beta+\lambda+1)(j-\gamma+\lambda+1)(j-\mu+1)}{(2j+\lambda-\mu+1)(2j+\lambda-\mu+2)}}
M_{j} = -\frac{(j-\alpha+\lambda+1)(j-\beta+\lambda+1)(j-\gamma+\lambda+1)(j-\mu+1)}{(2j+\lambda-\mu+1)(2j+\lambda-\mu+2)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
M[j] = -((j - alpha + lambda + 1)*(j - beta + lambda + 1)*(j - gamma + lambda + 1)*(j - mu + 1))/((2*j + lambda - mu + 1)*(2*j + lambda - mu + 2))
 
Subscript[M, j] == -Divide[(j - \[Alpha]+ \[Lambda]+ 1)*(j - \[Beta]+ \[Lambda]+ 1)*(j - \[Gamma]+ \[Lambda]+ 1)*(j - \[Mu]+ 1),(2*j + \[Lambda]- \[Mu]+ 1)*(2*j + \[Lambda]- \[Mu]+ 2)]
 Skipped - no semantic math Skipped - no semantic math - -
31.11.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M_{-1}P_{-1} = 0}
M_{-1}P_{-1} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
M[- 1]*P[- 1] = 0
 
Subscript[M, - 1]*Subscript[P, - 1] == 0
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda = \alpha}
\lambda = \alpha		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
lambda = alpha
 
\[Lambda] == \[Alpha]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = \beta-\epsilon}
\mu = \beta-\epsilon		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
mu = beta - epsilon
 
\[Mu] == \[Beta]- \[Epsilon]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda = \beta}
\lambda = \beta		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
lambda = beta
 
\[Lambda] == \[Beta]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = \alpha-\epsilon}
\mu = \alpha-\epsilon		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
mu = alpha - epsilon
 
\[Mu] == \[Alpha]- \[Epsilon]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda = \gamma+\delta-1}
\lambda = \gamma+\delta-1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
lambda = gamma + delta - 1
 
\[Lambda] == \[Gamma]+ \[Delta]- 1
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = 0}
\mu = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
mu = 0
 
\[Mu] == 0
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda = \gamma}
\lambda = \gamma		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
lambda = gamma
 
\[Lambda] == \[Gamma]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = \delta-1}
\mu = \delta-1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
mu = delta - 1
 
\[Mu] == \[Delta]- 1
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda = \delta}
\lambda = \delta		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
lambda = delta
 
\[Lambda] == \[Delta]
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = \gamma-1}
\mu = \gamma-1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
mu = gamma - 1
 
\[Mu] == \[Gamma]- 1
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda = 1}
\lambda = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
lambda = 1
 
\[Lambda] == 1
 Skipped - no semantic math Skipped - no semantic math - -
31.11#Ex12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = \gamma+\delta-2}
\mu = \gamma+\delta-2		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
mu = gamma + delta - 2
 
\[Mu] == \[Gamma]+ \[Delta]- 2
 Skipped - no semantic math Skipped - no semantic math - -
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