About Equation BSJ.2.1.2.4 |
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LaTeX encoding |
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u (2 n + 1) = 0
u (2 n) = \frac{(-1)^{n}}{2^{\nu} 4^{n} \Gamma (n + 1) \Gamma (n + \nu + 1)}
Maple encoding |
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u(2*n+1) = 0
u(2*n) = 2^(-nu)*4^(-n)*(-1)^n/GAMMA(n+1)/GAMMA(n+nu+1)
MathML encoding |
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<math xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow xref='id9'><mrow xref='id7'><mi xref='id1'>u</mi><mo>⁡</mo><mfenced><mrow xref='id6'><mrow xref='id4'><mn xref='id2'>2</mn><mo>⁢</mo><mi xref='id3'>n</mi></mrow><mo>+</mo><mn xref='id5'>1</mn></mrow></mfenced></mrow><mo>=</mo><mn xref='id8'>0</mn></mrow><annotation-xml encoding='MathML-Content'><apply id='id9'><eq/><apply id='id7'><ci id='id1'>u</ci><apply id='id6'><plus/><apply id='id4'><times/><cn id='id2' type='integer'>2</cn><ci id='id3'>n</ci></apply><cn id='id5' type='integer'>1</cn></apply></apply><cn id='id8' type='integer'>0</cn></apply></annotation-xml><annotation encoding='Maple'>u(2*n+1) = 0</annotation></semantics></math>
<math xmlns='http://www.w3.org/1998/Math/MathML'><semantics><mrow xref='id31'><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='id30'><mfrac><mrow xref='id17'><mrow><mrow xref='id9'><msup><mn xref='id6'>2</mn><mfenced><mrow xref='id8'><mo>-</mo><mi xref='id7'>ν</mi></mrow></mfenced></msup></mrow><mo>⁢</mo><mrow xref='id13'><msup><mn xref='id10'>4</mn><mfenced><mrow xref='id12'><mo>-</mo><mi xref='id11'>n</mi></mrow></mfenced></msup></mrow></mrow><mo>⁢</mo><mrow xref='id16'><msup><mfenced><mn xref='id14'>-1</mn></mfenced><mi xref='id15'>n</mi></msup></mrow></mrow><mrow xref='id29'><mrow xref='id22'><mi>Γ</mi><mo>⁡</mo><mfenced><mrow xref='id21'><mi xref='id19'>n</mi><mo>+</mo><mn xref='id20'>1</mn></mrow></mfenced></mrow><mo>⁢</mo><mrow xref='id28'><mi>Γ</mi><mo>⁡</mo><mfenced><mrow xref='id27'><mi xref='id24'>n</mi><mo>+</mo><mi xref='id25'>ν</mi><mo>+</mo><mn xref='id26'>1</mn></mrow></mfenced></mrow></mrow></mfrac></mrow></mrow><annotation-xml encoding='MathML-Content'><apply id='id31'><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='id30'><divide/><apply id='id17'><times/><apply id='id9'><power/><cn id='id6' type='integer'>2</cn><apply id='id8'><minus/><ci id='id7'>nu</ci></apply></apply><apply id='id13'><power/><cn id='id10' type='integer'>4</cn><apply id='id12'><minus/><ci id='id11'>n</ci></apply></apply><apply id='id16'><power/><cn id='id14' type='integer'>-1</cn><ci id='id15'>n</ci></apply></apply><apply id='id29'><times/><apply id='id22'><csymbol id='id18' definitionURL='http://www.maplesoft.com/MathML/GAMMA'>GAMMA</csymbol><apply id='id21'><plus/><ci id='id19'>n</ci><cn id='id20' type='integer'>1</cn></apply></apply><apply id='id28'><csymbol id='id23' definitionURL='http://www.maplesoft.com/MathML/GAMMA'>GAMMA</csymbol><apply id='id27'><plus/><ci id='id24'>n</ci><ci id='id25'>nu</ci><cn id='id26' type='integer'>1</cn></apply></apply></apply></apply></apply></annotation-xml><annotation encoding='Maple'>u(2*n) = 2^(-nu)*4^(-n)*(-1)^n/GAMMA(n+1)/GAMMA(n+nu+1)</annotation></semantics></math>