DLMF:13.6.E18 (Q4405): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10922 / rank
 
Normal rank
Property / Symbols used: Q10922 / qualifier
 
Defining formula:

H n ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}

\HermitepolyH{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q10922 / qualifier
 
xml-id: C18.S3.T1.t1.r13.m2abdec
Property / Symbols used
 
Property / Symbols used: Kummer confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Kummer confluent hypergeometric function / qualifier
 
Defining formula:

U ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

\KummerconfhyperU@{\NVar{a}}{\NVar{b}}{\NVar{z}}
Property / Symbols used: Kummer confluent hypergeometric function / qualifier
 
xml-id: C13.S2.E6.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q11559 / rank
 
Normal rank
Property / Symbols used: Q11559 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11559 / qualifier
 
xml-id: C13.S1.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1qdec

Latest revision as of 15:53, 2 January 2020

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DLMF:13.6.E18
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    Statements

    U ( 1 2 - 1 2 n , 3 2 , z 2 ) = 2 - n z - 1 H n ( z ) . Kummer-confluent-hypergeometric-U 1 2 1 2 𝑛 3 2 superscript 𝑧 2 superscript 2 𝑛 superscript 𝑧 1 Hermite-polynomial-H 𝑛 𝑧 {\displaystyle{\displaystyle U\left(\tfrac{1}{2}-\tfrac{1}{2}n,\tfrac{3}{2},z^% {2}\right)=2^{-n}z^{-1}H_{n}\left(z\right).}}
    0 references
    DLMF:13.6.E18
    0 references
    H n ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r13.m2abdec
    0 references
    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.m2ahdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C13.S1.XMD2.m1bdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C13.S1.XMD6.m1qdec
    0 references