DLMF:15.4.E5 (Q4988): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(One intermediate revision by the same user not shown)
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: Q11644 / rank
 
Normal rank
Property / Symbols used: Q11644 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11644 / qualifier
 
xml-id: C15.S1.XMD3.m1ddec

Latest revision as of 12:47, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:15.4.E5
No description defined

    Statements

    test
    F ⁡ ( 1 2 , 1 2 ; 3 2 ; - z 2 ) = z - 1 ⁢ ln ⁡ ( z + 1 + z 2 ) . Gauss-hypergeometric-F 1 2 1 2 3 2 superscript 𝑧 2 superscript 𝑧 1 𝑧 1 superscript 𝑧 2 {\displaystyle{\displaystyle F\left(\tfrac{1}{2},\tfrac{1}{2};\tfrac{3}{2};-z^% {2}\right)=z^{-1}\ln\left(z+\sqrt{1+z^{2}}\right).}}
    0 references
    DLMF id
    DLMF:15.4.E5
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    test
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2addec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1ddec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q4988&oldid=28326"