DLMF:2.6.E57 (Q883): Difference between revisions

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‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11040 / rank
 
Normal rank
Property / Symbols used: Q11040 / qualifier
 
Defining formula:

a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}

a_{n}
Property / Symbols used: Q11040 / qualifier
 
xml-id: C2.S6.XMD28.m1adec
Property / Symbols used
 
Property / Symbols used: Q11041 / rank
 
Normal rank
Property / Symbols used: Q11041 / qualifier
 
Defining formula:

b n subscript 𝑏 𝑛 {\displaystyle{\displaystyle b_{n}}}

b_{n}
Property / Symbols used: Q11041 / qualifier
 
xml-id: C2.S6.XMD29.m1adec
Property / Symbols used
 
Property / Symbols used: Q11038 / rank
 
Normal rank
Property / Symbols used: Q11038 / qualifier
 
Defining formula:

h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}

h(x)
Property / Symbols used: Q11038 / qualifier
 
xml-id: C2.S6.XMD30.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11022 / rank
 
Normal rank
Property / Symbols used: Q11022 / qualifier
 
Defining formula:

f n , n ⁢ ( t ) subscript 𝑓 𝑛 𝑛 𝑡 {\displaystyle{\displaystyle f_{n,n}(t)}}

f_{n,n}(t)
Property / Symbols used: Q11022 / qualifier
 
xml-id: C2.S6.XMD7.m1ndec

Latest revision as of 17:19, 1 January 2020

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DLMF:2.6.E57
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    Statements

    Defining formula
    f ⁢ ( t ) ⁢ h ⁢ ( x ⁢ t ) = ∑ j = 0 n - 1 ∑ k = 0 n - 1 a j ⁢ b k ⁢ t j + α - 1 - k - β ⁢ x - k - β + ∑ j = 0 n - 1 a j ⁢ t j + α - 1 ⁢ h n ⁢ ( x ⁢ t ) + ∑ k = 0 n - 1 b k ⁢ x - k - β ⁢ t - k - β ⁢ f n ⁢ ( t ) + f n ⁢ ( t ) ⁢ h n ⁢ ( x ⁢ t ) . 𝑓 𝑡 ℎ 𝑥 𝑡 superscript subscript 𝑗 0 𝑛 1 superscript subscript 𝑘 0 𝑛 1 subscript 𝑎 𝑗 subscript 𝑏 𝑘 superscript 𝑡 𝑗 𝛼 1 𝑘 𝛽 superscript 𝑥 𝑘 𝛽 superscript subscript 𝑗 0 𝑛 1 subscript 𝑎 𝑗 superscript 𝑡 𝑗 𝛼 1 subscript ℎ 𝑛 𝑥 𝑡 superscript subscript 𝑘 0 𝑛 1 subscript 𝑏 𝑘 superscript 𝑥 𝑘 𝛽 superscript 𝑡 𝑘 𝛽 subscript 𝑓 𝑛 𝑡 subscript 𝑓 𝑛 𝑡 subscript ℎ 𝑛 𝑥 𝑡 {\displaystyle{\displaystyle f(t)h(xt)=\sum_{j=0}^{n-1}\sum_{k=0}^{n-1}a_{j}b_% {k}t^{j+\alpha-1-k-\beta}x^{-k-\beta}+\sum_{j=0}^{n-1}a_{j}t^{j+\alpha-1}h_{n}% (xt)+\sum_{k=0}^{n-1}b_{k}x^{-k-\beta}t^{-k-\beta}f_{n}(t)+f_{n}(t)h_{n}(xt).}}
    0 references
    DLMF id
    DLMF:2.6.E57
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    Q11019
    Defining formula
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1addec
    0 references
    Q11039
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S6.XMD27.m1bdec
    0 references
    Q11040
    Defining formula
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S6.XMD28.m1adec
    0 references
    Q11041
    Defining formula
    b n subscript 𝑏 𝑛 {\displaystyle{\displaystyle b_{n}}}
    xml-id
    C2.S6.XMD29.m1adec
    0 references
    Q11038
    Defining formula
    h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}
    xml-id
    C2.S6.XMD30.m1bdec
    0 references
    Q11022
    Defining formula
    f n , n ⁢ ( t ) subscript 𝑓 𝑛 𝑛 𝑡 {\displaystyle{\displaystyle f_{n,n}(t)}}
    xml-id
    C2.S6.XMD7.m1ndec
    0 references
     
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