DLMF:11.4.E30 (Q3962): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2avdec
Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2acdec
Property / Symbols used
 
Property / Symbols used: modified Struve function / rank
 
Normal rank
Property / Symbols used: modified Struve function / qualifier
 
test:

𝐋 ν ( z ) modified-Struve-L 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{L}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modStruveL{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Struve function / qualifier
 
xml-id: C11.S2.E2.m2ajdec
Property / Symbols used
 
Property / Symbols used: Q11491 / rank
 
Normal rank
Property / Symbols used: Q11491 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11491 / qualifier
 
xml-id: C11.S1.XMD2.m1abdec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1odec

Latest revision as of 13:42, 2 January 2020

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DLMF:11.4.E30
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    Statements

    d d z ( z - ν 𝐋 ν ( z ) ) = 2 - ν π Γ ( ν + 3 2 ) + z - ν 𝐋 ν + 1 ( z ) . derivative 𝑧 superscript 𝑧 𝜈 modified-Struve-L 𝜈 𝑧 superscript 2 𝜈 𝜋 Euler-Gamma 𝜈 3 2 superscript 𝑧 𝜈 modified-Struve-L 𝜈 1 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\left(z^{-\nu}% \mathbf{L}_{\nu}\left(z\right)\right)=\frac{2^{-\nu}}{\sqrt{\pi}\Gamma\left(% \nu+\tfrac{3}{2}\right)}+z^{-\nu}\mathbf{L}_{\nu+1}\left(z\right).}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2ahdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2avdec
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    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2acdec
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    𝐋 ν ( z ) modified-Struve-L 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{L}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C11.S2.E2.m2ajdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C11.S1.XMD2.m1abdec
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    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C11.S1.XMD3.m1odec
    0 references