DLMF:13.4.E16 (Q4379): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aodec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2agdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aodec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1ahdec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1odec

Latest revision as of 14:49, 2 January 2020

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DLMF:13.4.E16
No description defined

    Statements

    test
    𝐌 ⁡ ( a , b , - z ) = 1 2 ⁢ π ⁢ i ⁢ Γ ⁡ ( a ) ⁢ ∫ - i ⁢ ∞ i ⁢ ∞ Γ ⁡ ( a + t ) ⁢ Γ ⁡ ( - t ) Γ ⁡ ( b + t ) ⁢ z t ⁢ d t , Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 1 2 𝜋 imaginary-unit Euler-Gamma 𝑎 superscript subscript imaginary-unit imaginary-unit Euler-Gamma 𝑎 𝑡 Euler-Gamma 𝑡 Euler-Gamma 𝑏 𝑡 superscript 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,-z\right)=\frac{1}{2\pi% \mathrm{i}\Gamma\left(a\right)}\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}% \frac{\Gamma\left(a+t\right)\Gamma\left(-t\right)}{\Gamma\left(b+t\right)}z^{t% }\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.4.E16
    0 references
    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{1}{2}\pi}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2amdec
    0 references
    Olver’s confluent hypergeometric function
    test
    𝐌 ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}
    xml-id
    C13.S2.E3.m2aidec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2agdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aodec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1ahdec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1odec
    0 references
     
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