DLMF:13.13.E7 (Q4484): Difference between revisions

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Property / constraint
 

| y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}

|y|<|x|
Property / constraint: | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Kummer confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Kummer confluent hypergeometric function / qualifier
 
test:

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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1afdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5afdec
Property / Symbols used
 
Property / Symbols used: Q11566 / rank
 
Normal rank
Property / Symbols used: Q11566 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11566 / qualifier
 
xml-id: C13.S1.XMD4.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11580 / rank
 
Normal rank
Property / Symbols used: Q11580 / qualifier
 
test:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11580 / qualifier
 
xml-id: C13.S1.XMD5.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11559 / rank
 
Normal rank
Property / Symbols used: Q11559 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11559 / qualifier
 
xml-id: C13.S1.XMD2.m1fdec

Latest revision as of 15:04, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.13.E7
No description defined

    Statements

    test
    ∑ n = 0 ∞ ( a ) n ⁢ ( - y ) n n ! ⁢ U ⁡ ( a + n , b + n , x ) , superscript subscript 𝑛 0 Pochhammer 𝑎 𝑛 superscript 𝑦 𝑛 𝑛 Kummer-confluent-hypergeometric-U 𝑎 𝑛 𝑏 𝑛 𝑥 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{{\left(a\right)_{n}}(-y)^% {n}}{n!}U\left(a+n,b+n,x\right),}}
    0 references
    DLMF id
    DLMF:13.13.E7
    0 references
    constraint
    | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}
    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.m2adec
    0 references
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1afdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5afdec
    0 references
    Q11566
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1fdec
    0 references
    Q11580
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C13.S1.XMD5.m1fdec
    0 references
    Q11559
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1fdec
    0 references
     
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