DLMF:13.3.E26 (Q4360)

From testwiki
Revision as of 14:44, 2 January 2020 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:13.3.E26
No description defined

    Statements

    test
    ( z ⁢ d d z ⁡ z ) n ⁢ ( z b - a - 1 ⁢ e - z ⁢ U ⁡ ( a , b , z ) ) = ( - 1 ) n ⁢ z b - a + n - 1 ⁢ e - z ⁢ U ⁡ ( a - n , b , z ) , superscript 𝑧 derivative 𝑧 𝑧 𝑛 superscript 𝑧 𝑏 𝑎 1 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 1 𝑛 superscript 𝑧 𝑏 𝑎 𝑛 1 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝑎 𝑛 𝑏 𝑧 {\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(z^{b-a-1}e^{-z}U\left(a,b,z\right)\right)=(-1)^{n}z^{b-a+n-1}e^{-z}U% \left(a-n,b,z\right),}}
    0 references
    DLMF id
    DLMF:13.3.E26
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    test
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2akdec
    0 references
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2akdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q4360&oldid=23533"