DLMF:10.45.E8 (Q3665): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: modified Bessel function fo the second kind of imaginary order / rank
 
Normal rank
Property / Symbols used: modified Bessel function fo the second kind of imaginary order / qualifier
 
test:

K ~ Ξ½ ⁑ ( x ) modified-Bessel-second-kind-imaginary-order 𝜈 π‘₯ {\displaystyle{\displaystyle\widetilde{K}_{\NVar{\nu}}\left(\NVar{x}\right)}}

\modBesselKimag{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: modified Bessel function fo the second kind of imaginary order / qualifier
 
xml-id: C10.S45.E2.m3aedec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁑ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
test:

x π‘₯ {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1gdec

Latest revision as of 14:07, 2 January 2020

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DLMF:10.45.E8
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    Statements

    K ~ 0 ⁑ ( x ) = K 0 ⁑ ( x ) = - ln ⁑ ( 1 2 ⁒ x ) - Ξ³ + O ⁑ ( x 2 ⁒ ln ⁑ x ) , modified-Bessel-second-kind-imaginary-order 0 π‘₯ modified-Bessel-second-kind 0 π‘₯ 1 2 π‘₯ Big-O superscript π‘₯ 2 π‘₯ {\displaystyle{\displaystyle\widetilde{K}_{0}\left(x\right)=K_{0}\left(x\right% )=-\ln\left(\tfrac{1}{2}x\right)-\gamma+O\left(x^{2}\ln x\right),}}
    0 references
    0 references
    O ⁑ ( x ) Big-O π‘₯ {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2acdec
    0 references
    Ξ³ {\displaystyle{\displaystyle\gamma}}
    C5.S2.E3.m2adec
    0 references
    K Ξ½ ⁑ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.E3.m2aadec
    0 references
    K ~ Ξ½ ⁑ ( x ) modified-Bessel-second-kind-imaginary-order 𝜈 π‘₯ {\displaystyle{\displaystyle\widetilde{K}_{\NVar{\nu}}\left(\NVar{x}\right)}}
    C10.S45.E2.m3aedec
    0 references
    ln ⁑ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2abdec
    0 references
    x π‘₯ {\displaystyle{\displaystyle x}}
    C10.S1.XMD4.m1gdec
    0 references