DLMF:12.2.E7 (Q4092): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11320 / rank
 
Normal rank
Property / Symbols used: Q11320 / qualifier
 
Defining formula:

U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}

\paraU@{\NVar{a}}{\NVar{z}}
Property / Symbols used: Q11320 / qualifier
 
xml-id: C12.S2.SS1.p1.m1abdec

Revision as of 15:04, 2 January 2020

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DLMF:12.2.E7
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    Statements

    Defining formula
    U ′ ⁡ ( a , 0 ) = - π 2 1 2 ⁢ a - 1 4 ⁢ Γ ⁡ ( 1 4 + 1 2 ⁢ a ) , diffop parabolic-U 1 𝑎 0 𝜋 superscript 2 1 2 𝑎 1 4 Euler-Gamma 1 4 1 2 𝑎 {\displaystyle{\displaystyle U'\left(a,0\right)=-\frac{\sqrt{\pi}}{2^{\frac{1}% {2}a-\frac{1}{4}}\Gamma\left(\frac{1}{4}+\frac{1}{2}a\right)},}}
    0 references
    DLMF id
    DLMF:12.2.E7
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q11320
    Defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1abdec
    0 references
     
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