View source for 30.9

{{DISPLAYTITLE:Spheroidal Wave Functions - 30.9 Asymptotic Approximations and Expansions}}

<div style="width: 100%; height: 75vh; overflow: auto;">
{| class="wikitable sortable" style="margin: 0;"
|-
! scope="col" style="position: sticky; top: 0;" | DLMF 
! scope="col" style="position: sticky; top: 0;" | Formula 
! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/30.9#Ex5 30.9#Ex5] || <math qid="Q8883">2^{16}\beta_{4} = -63q^{6}-4940q^{4}-43327q^{2}-22470+128m^{2}(115q^{4}+1310q^{2}+735)-24576m^{4}(q^{2}+1)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2^{16}\beta_{4} = -63q^{6}-4940q^{4}-43327q^{2}-22470+128m^{2}(115q^{4}+1310q^{2}+735)-24576m^{4}(q^{2}+1)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/30.9#Ex6 30.9#Ex6] || <math qid="Q8884">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</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>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</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/30.9#Ex7 30.9#Ex7] || <math qid="Q8886">2c_{0} = -q^{2}-1+m^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2c_{0} = -q^{2}-1+m^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*c[0] = - (q)^(2)- 1 + (m)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*Subscript[c, 0] == - (q)^(2)- 1 + (m)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/30.9#Ex8 30.9#Ex8] || <math qid="Q8887">8c_{1} = -q^{3}-q+m^{2}q</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>8c_{1} = -q^{3}-q+m^{2}q</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">8*c[1] = - (q)^(3)- q + (m)^(2)* q</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">8*Subscript[c, 1] == - (q)^(3)- q + (m)^(2)* q</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/30.9#Ex9 30.9#Ex9] || <math qid="Q8888">2^{6}c_{2} = -5q^{4}-10q^{2}-1+2m^{2}(3q^{2}+1)-m^{4}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2^{6}c_{2} = -5q^{4}-10q^{2}-1+2m^{2}(3q^{2}+1)-m^{4}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(6)* c[2] = - 5*(q)^(4)- 10*(q)^(2)- 1 + 2*(m)^(2)*(3*(q)^(2)+ 1)- (m)^(4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(6)* Subscript[c, 2] == - 5*(q)^(4)- 10*(q)^(2)- 1 + 2*(m)^(2)*(3*(q)^(2)+ 1)- (m)^(4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/30.9#Ex10 30.9#Ex10] || <math qid="Q8889">2^{9}c_{3} = -33q^{5}-114q^{3}-37q+2m^{2}(23q^{3}+25q)-13m^{4}q</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2^{9}c_{3} = -33q^{5}-114q^{3}-37q+2m^{2}(23q^{3}+25q)-13m^{4}q</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(9)* c[3] = - 33*(q)^(5)- 114*(q)^(3)- 37*q + 2*(m)^(2)*(23*(q)^(3)+ 25*q)- 13*(m)^(4)* q</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/30.9#Ex11 30.9#Ex11] || <math qid="Q8890">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}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>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}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/30.9#Ex12 30.9#Ex12] || <math qid="Q8891">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</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>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</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(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</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|}
</div>