DLMF:13.5.E1 (Q4382): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / qualifier
 
Defining formula:

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

\KummerconfhyperM@{\NVar{a}}{\NVar{b}}{\NVar{z}}
Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / qualifier
 
xml-id: C13.S2.E2.m2adec
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q11563 / rank
 
Normal rank
Property / Symbols used: Q11563 / qualifier
 
Defining formula:

u n subscript 𝑢 𝑛 {\displaystyle{\displaystyle u_{n}}}

u_{n}
Property / Symbols used: Q11563 / qualifier
 
xml-id: C13.S5.XMD1.m1dec

Latest revision as of 15:50, 2 January 2020

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DLMF:13.5.E1
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    Statements

    Defining formula
    M ⁡ ( a , b , z ) M ⁡ ( a + 1 , b + 1 , z ) = 1 + u 1 ⁢ z 1 + u 2 ⁢ z 1 + ⋯ , Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 Kummer-confluent-hypergeometric-M 𝑎 1 𝑏 1 𝑧 1 continued-fraction subscript 𝑢 1 𝑧 1 continued-fraction subscript 𝑢 2 𝑧 1 ⋯ {\displaystyle{\displaystyle\frac{M\left(a,b,z\right)}{M\left(a+1,b+1,z\right)% }=1+\cfrac{u_{1}z}{1+\cfrac{u_{2}z}{1+\cdots}},}}
    0 references
    DLMF id
    DLMF:13.5.E1
    0 references
    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    Defining formula
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2adec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1dec
    0 references
    Q11563
    Defining formula
    u n subscript 𝑢 𝑛 {\displaystyle{\displaystyle u_{n}}}
    xml-id
    C13.S5.XMD1.m1dec
    0 references
     
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