DLMF:13.6.E13 (Q4400): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q11320 / rank
 
Normal rank
Property / Symbols used: Q11320 / qualifier
 
test:

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.m1aadec
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.m1ldec

Latest revision as of 14:52, 2 January 2020

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DLMF:13.6.E13
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    Statements

    U ( 1 2 a + 3 4 , 3 2 , 1 2 z 2 ) = 2 1 2 a + 3 4 e 1 4 z 2 z U ( a , z ) . Kummer-confluent-hypergeometric-U 1 2 𝑎 3 4 3 2 1 2 superscript 𝑧 2 superscript 2 1 2 𝑎 3 4 superscript 𝑒 1 4 superscript 𝑧 2 𝑧 parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},% \tfrac{1}{2}z^{2}\right)=2^{\frac{1}{2}a+\frac{3}{4}}\frac{e^{\frac{1}{4}z^{2}% }}{z}U\left(a,z\right).}}
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    U ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    C13.S2.E6.m2agdec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2ahdec
    0 references
    U ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    C12.S2.SS1.p1.m1aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C13.S1.XMD6.m1ldec
    0 references