Spheroidal Wave Functions - 30.9 Asymptotic Approximations and Expansions
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 30.9#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{16}\beta_{4} = -63q^{6}-4940q^{4}-43327q^{2}-22470+128m^{2}(115q^{4}+1310q^{2}+735)-24576m^{4}(q^{2}+1)}
2^{16}\beta_{4} = -63q^{6}-4940q^{4}-43327q^{2}-22470+128m^{2}(115q^{4}+1310q^{2}+735)-24576m^{4}(q^{2}+1) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (2)^(16)* beta[4] = - 63*(q)^(6)- 4940*(q)^(4)- 43327*(q)^(2)- 22470 + 128*(m)^(2)*(115*(q)^(4)+ 1310*(q)^(2)+ 735)- 24576*(m)^(4)*((q)^(2)+ 1) |
(2)^(16)* Subscript[\[Beta], 4] == - 63*(q)^(6)- 4940*(q)^(4)- 43327*(q)^(2)- 22470 + 128*(m)^(2)*(115*(q)^(4)+ 1310*(q)^(2)+ 735)- 24576*(m)^(4)*((q)^(2)+ 1) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 30.9#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{20}\beta_{5} = -527q^{7}-61529q^{5}-10\;43961q^{3}-22\;41599q+32m^{2}(5739q^{5}+1\;27550q^{3}+2\;98951q)-2048m^{4}(355q^{3}+1505q)+65536m^{6}q}
2^{20}\beta_{5} = -527q^{7}-61529q^{5}-10\;43961q^{3}-22\;41599q+32m^{2}(5739q^{5}+1\;27550q^{3}+2\;98951q)-2048m^{4}(355q^{3}+1505q)+65536m^{6}q |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (2)^(20)* beta[5] = - 527*(q)^(7)- 61529*(q)^(5)- 1043961*(q)^(3)- 2241599*q + 32*(m)^(2)*(5739*(q)^(5)+ 127550*(q)^(3)+ 298951*q)- 2048*(m)^(4)*(355*(q)^(3)+ 1505*q)+ 65536*(m)^(6)* q |
(2)^(20)* Subscript[\[Beta], 5] == - 527*(q)^(7)- 61529*(q)^(5)- 1043961*(q)^(3)- 2241599*q + 32*(m)^(2)*(5739*(q)^(5)+ 127550*(q)^(3)+ 298951*q)- 2048*(m)^(4)*(355*(q)^(3)+ 1505*q)+ 65536*(m)^(6)* q |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 30.9#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2c_{0} = -q^{2}-1+m^{2}}
2c_{0} = -q^{2}-1+m^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 2*c[0] = - (q)^(2)- 1 + (m)^(2) |
2*Subscript[c, 0] == - (q)^(2)- 1 + (m)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 30.9#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 8c_{1} = -q^{3}-q+m^{2}q}
8c_{1} = -q^{3}-q+m^{2}q |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 8*c[1] = - (q)^(3)- q + (m)^(2)* q |
8*Subscript[c, 1] == - (q)^(3)- q + (m)^(2)* q |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 30.9#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{6}c_{2} = -5q^{4}-10q^{2}-1+2m^{2}(3q^{2}+1)-m^{4}}
2^{6}c_{2} = -5q^{4}-10q^{2}-1+2m^{2}(3q^{2}+1)-m^{4} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (2)^(6)* c[2] = - 5*(q)^(4)- 10*(q)^(2)- 1 + 2*(m)^(2)*(3*(q)^(2)+ 1)- (m)^(4) |
(2)^(6)* Subscript[c, 2] == - 5*(q)^(4)- 10*(q)^(2)- 1 + 2*(m)^(2)*(3*(q)^(2)+ 1)- (m)^(4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 30.9#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{9}c_{3} = -33q^{5}-114q^{3}-37q+2m^{2}(23q^{3}+25q)-13m^{4}q}
2^{9}c_{3} = -33q^{5}-114q^{3}-37q+2m^{2}(23q^{3}+25q)-13m^{4}q |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (2)^(9)* c[3] = - 33*(q)^(5)- 114*(q)^(3)- 37*q + 2*(m)^(2)*(23*(q)^(3)+ 25*q)- 13*(m)^(4)* q |
(2)^(9)* Subscript[c, 3] == - 33*(q)^(5)- 114*(q)^(3)- 37*q + 2*(m)^(2)*(23*(q)^(3)+ 25*q)- 13*(m)^(4)* q |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 30.9#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{10}c_{4} = -63q^{6}-340q^{4}-239q^{2}-14+10m^{2}(10q^{4}+23q^{2}+3)-3m^{4}(13q^{2}+6)+2m^{6}}
2^{10}c_{4} = -63q^{6}-340q^{4}-239q^{2}-14+10m^{2}(10q^{4}+23q^{2}+3)-3m^{4}(13q^{2}+6)+2m^{6} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (2)^(10)* c[4] = - 63*(q)^(6)- 340*(q)^(4)- 239*(q)^(2)- 14 + 10*(m)^(2)*(10*(q)^(4)+ 23*(q)^(2)+ 3)- 3*(m)^(4)*(13*(q)^(2)+ 6)+ 2*(m)^(6) |
(2)^(10)* Subscript[c, 4] == - 63*(q)^(6)- 340*(q)^(4)- 239*(q)^(2)- 14 + 10*(m)^(2)*(10*(q)^(4)+ 23*(q)^(2)+ 3)- 3*(m)^(4)*(13*(q)^(2)+ 6)+ 2*(m)^(6) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 30.9#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{13}c_{5} = -527q^{7}-4139q^{5}-5221q^{3}-1009q+m^{2}(939q^{5}+3750q^{3}+1591q)-m^{4}(465q^{3}+635q)+53m^{6}q}
2^{13}c_{5} = -527q^{7}-4139q^{5}-5221q^{3}-1009q+m^{2}(939q^{5}+3750q^{3}+1591q)-m^{4}(465q^{3}+635q)+53m^{6}q |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (2)^(13)* c[5] = - 527*(q)^(7)- 4139*(q)^(5)- 5221*(q)^(3)- 1009*q + (m)^(2)*(939*(q)^(5)+ 3750*(q)^(3)+ 1591*q)- (m)^(4)*(465*(q)^(3)+ 635*q)+ 53*(m)^(6)* q |
(2)^(13)* Subscript[c, 5] == - 527*(q)^(7)- 4139*(q)^(5)- 5221*(q)^(3)- 1009*q + (m)^(2)*(939*(q)^(5)+ 3750*(q)^(3)+ 1591*q)- (m)^(4)*(465*(q)^(3)+ 635*q)+ 53*(m)^(6)* q |
Skipped - no semantic math | Skipped - no semantic math | - | - |