Heun Functions - 31.16 Mathematical Applications
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 31.16.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P_{j}A_{j-1}+Q_{j}A_{j}+R_{j}A_{j+1} = 0}
P_{j}A_{j-1}+Q_{j}A_{j}+R_{j}A_{j+1} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle j = 1} | (((epsilon - j + n)*j*(beta + j - 1)*(gamma + delta + j - 2))/((gamma + delta + 2*j - 3)*(gamma + delta + 2*j - 2)))*A[j - 1]+(- a*j*(j + gamma + delta - 1)- q +((j - n)*(j + beta)*(j + gamma)*(j + gamma + delta - 1))/((2*j + gamma + delta)*(2*j + gamma + delta - 1))+((j + n + gamma + delta - 1)*j*(j + delta - 1)*(j - beta + gamma + delta - 1))/((2*j + gamma + delta - 1)*(2*j + gamma + delta - 2)))*A[j]+(((n - j)*(j + n + gamma + delta)*(j + gamma)*(j + delta))/((gamma + delta + 2*j)*(gamma + delta + 2*j + 1)))*A[j + 1] = 0 |
(Divide[(\[Epsilon]- j + n)*j*(\[Beta]+ j - 1)*(\[Gamma]+ \[Delta]+ j - 2),(\[Gamma]+ \[Delta]+ 2*j - 3)*(\[Gamma]+ \[Delta]+ 2*j - 2)])*Subscript[A, j - 1]+(- a*j*(j + \[Gamma]+ \[Delta]- 1)- q +Divide[(j - n)*(j + \[Beta])*(j + \[Gamma])*(j + \[Gamma]+ \[Delta]- 1),(2*j + \[Gamma]+ \[Delta])*(2*j + \[Gamma]+ \[Delta]- 1)]+Divide[(j + n + \[Gamma]+ \[Delta]- 1)*j*(j + \[Delta]- 1)*(j - \[Beta]+ \[Gamma]+ \[Delta]- 1),(2*j + \[Gamma]+ \[Delta]- 1)*(2*j + \[Gamma]+ \[Delta]- 2)])*Subscript[A, j]+(Divide[(n - j)*(j + n + \[Gamma]+ \[Delta])*(j + \[Gamma])*(j + \[Delta]),(\[Gamma]+ \[Delta]+ 2*j)*(\[Gamma]+ \[Delta]+ 2*j + 1)])*Subscript[A, j + 1] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |