ESF - The Encyclopedia of Special Functions

About Equation SI.2.1.2.4

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$\begin{equation*} \begin{split} u (2 n + 1)& =0 \end{split} \end{equation*}$

$\begin{equation*} \begin{split} u (2 n)& =\frac{(-1)^{n}}{(2 n + 1) \Gamma (2 n + 2)} \end{split} \end{equation*}$

Absolute reference: SI:asympt:0:RDINREFRDGENFROMRDCLOSED

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u (2 n + 1) = 0

u (2 n) = \frac{(-1)^{n}}{(2 n + 1) \Gamma (2 n + 2)}

Maple encoding

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u(2*n+1) = 0

u(2*n) = 1/(2*n+1)/GAMMA(2*n+2)*(-1)^n

<math xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow xref='id23'><mrow xref='id5'><mi xref='id1'>u</mi><mo>⁡</mo><mfenced><mrow xref='id4'><mn xref='id2'>2</mn><mo>⁢</mo><mi xref='id3'>n</mi></mrow></mfenced></mrow><mo>=</mo><mrow xref='id22'><mfrac><mrow xref='id8'><msup><mfenced><mn xref='id6'>-1</mn></mfenced><mi xref='id7'>n</mi></msup></mrow><mrow xref='id21'><mfenced><mrow xref='id13'><mrow xref='id11'><mn xref='id9'>2</mn><mo>⁢</mo><mi xref='id10'>n</mi></mrow><mo>+</mo><mn xref='id12'>1</mn></mrow></mfenced><mo>⁢</mo><mrow xref='id20'><mi>Γ</mi><mo>⁡</mo><mfenced><mrow xref='id19'><mrow xref='id17'><mn xref='id15'>2</mn><mo>⁢</mo><mi xref='id16'>n</mi></mrow><mo>+</mo><mn xref='id18'>2</mn></mrow></mfenced></mrow></mrow></mfrac></mrow></mrow><annotation-xml encoding='MathML-Content'><apply id='id23'><eq/><apply id='id5'><ci id='id1'>u</ci><apply id='id4'><times/><cn id='id2' type='integer'>2</cn><ci id='id3'>n</ci></apply></apply><apply id='id22'><divide/><apply id='id8'><power/><cn id='id6' type='integer'>-1</cn><ci id='id7'>n</ci></apply><apply id='id21'><times/><apply id='id13'><plus/><apply id='id11'><times/><cn id='id9' type='integer'>2</cn><ci id='id10'>n</ci></apply><cn id='id12' type='integer'>1</cn></apply><apply id='id20'><csymbol id='id14' definitionURL='http://www.maplesoft.com/MathML/GAMMA'>GAMMA</csymbol><apply id='id19'><plus/><apply id='id17'><times/><cn id='id15' type='integer'>2</cn><ci id='id16'>n</ci></apply><cn id='id18' type='integer'>2</cn></apply></apply></apply></apply></apply></annotation-xml><annotation encoding='Maple'>u(2*n) = 1/(2*n+1)/GAMMA(2*n+2)*(-1)^n</annotation></semantics></math>

About Equation SI.2.1.2.4

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