Lamé Functions - 29.7 Asymptotic Expansions
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 29.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau_{0} = \frac{1}{2^{3}}(1+k^{2})(1+p^{2})}
\tau_{0} = \frac{1}{2^{3}}(1+k^{2})(1+p^{2}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tau[0] = (1)/((2)^(3))*(1 + (k)^(2))*(1 + (p)^(2)) |
Subscript[\[Tau], 0] == Divide[1,(2)^(3)]*(1 + (k)^(2))*(1 + (p)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau_{1} = \frac{p}{2^{6}}((1+k^{2})^{2}(p^{2}+3)-4k^{2}(p^{2}+5))}
\tau_{1} = \frac{p}{2^{6}}((1+k^{2})^{2}(p^{2}+3)-4k^{2}(p^{2}+5)) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tau[1] = (p)/((2)^(6))*((1 + (k)^(2))^(2)*((p)^(2)+ 3)- 4*(k)^(2)*((p)^(2)+ 5)) |
Subscript[\[Tau], 1] == Divide[p,(2)^(6)]*((1 + (k)^(2))^(2)*((p)^(2)+ 3)- 4*(k)^(2)*((p)^(2)+ 5)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.7.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau_{2} = \frac{1}{2^{10}}(1+k^{2})(1-k^{2})^{2}(5p^{4}+34p^{2}+9)}
\tau_{2} = \frac{1}{2^{10}}(1+k^{2})(1-k^{2})^{2}(5p^{4}+34p^{2}+9) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tau[2] = (1)/((2)^(10))*(1 + (k)^(2))*(1 - (k)^(2))^(2)*(5*(p)^(4)+ 34*(p)^(2)+ 9) |
Subscript[\[Tau], 2] == Divide[1,(2)^(10)]*(1 + (k)^(2))*(1 - (k)^(2))^(2)*(5*(p)^(4)+ 34*(p)^(2)+ 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.7.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau_{3} = \frac{p}{2^{14}}((1+k^{2})^{4}(33p^{4}+410p^{2}+405)-24k^{2}(1+k^{2})^{2}(7p^{4}+90p^{2}+95)+16k^{4}(9p^{4}+130p^{2}+173))}
\tau_{3} = \frac{p}{2^{14}}((1+k^{2})^{4}(33p^{4}+410p^{2}+405)-24k^{2}(1+k^{2})^{2}(7p^{4}+90p^{2}+95)+16k^{4}(9p^{4}+130p^{2}+173)) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tau[3] = (p)/((2)^(14))*((1 + (k)^(2))^(4)*(33*(p)^(4)+ 410*(p)^(2)+ 405)- 24*(k)^(2)*(1 + (k)^(2))^(2)*(7*(p)^(4)+ 90*(p)^(2)+ 95)+ 16*(k)^(4)*(9*(p)^(4)+ 130*(p)^(2)+ 173)) |
Subscript[\[Tau], 3] == Divide[p,(2)^(14)]*((1 + (k)^(2))^(4)*(33*(p)^(4)+ 410*(p)^(2)+ 405)- 24*(k)^(2)*(1 + (k)^(2))^(2)*(7*(p)^(4)+ 90*(p)^(2)+ 95)+ 16*(k)^(4)*(9*(p)^(4)+ 130*(p)^(2)+ 173)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 29.7.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau_{4} = \frac{1}{2^{16}}((1+k^{2})^{5}(63p^{6}+1260p^{4}+2943p^{2}+486)-8k^{2}(1+k^{2})^{3}(49p^{6}+1010p^{4}+2493p^{2}+432)+16k^{4}(1+k^{2})(35p^{6}+760p^{4}+2043p^{2}+378))}
\tau_{4} = \frac{1}{2^{16}}((1+k^{2})^{5}(63p^{6}+1260p^{4}+2943p^{2}+486)-8k^{2}(1+k^{2})^{3}(49p^{6}+1010p^{4}+2493p^{2}+432)+16k^{4}(1+k^{2})(35p^{6}+760p^{4}+2043p^{2}+378)) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tau[4] = (1)/((2)^(16))*((1 + (k)^(2))^(5)*(63*(p)^(6)+ 1260*(p)^(4)+ 2943*(p)^(2)+ 486)- 8*(k)^(2)*(1 + (k)^(2))^(3)*(49*(p)^(6)+ 1010*(p)^(4)+ 2493*(p)^(2)+ 432)+ 16*(k)^(4)*(1 + (k)^(2))*(35*(p)^(6)+ 760*(p)^(4)+ 2043*(p)^(2)+ 378)) |
Subscript[\[Tau], 4] == Divide[1,(2)^(16)]*((1 + (k)^(2))^(5)*(63*(p)^(6)+ 1260*(p)^(4)+ 2943*(p)^(2)+ 486)- 8*(k)^(2)*(1 + (k)^(2))^(3)*(49*(p)^(6)+ 1010*(p)^(4)+ 2493*(p)^(2)+ 432)+ 16*(k)^(4)*(1 + (k)^(2))*(35*(p)^(6)+ 760*(p)^(4)+ 2043*(p)^(2)+ 378)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |