DLMF:18.22.E14 (Q5883): Difference between revisions

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‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1aadec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1ndec
Property / Symbols used
 
Property / Symbols used: Q11731 / rank
 
Normal rank
Property / Symbols used: Q11731 / qualifier
 
Defining formula:

p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}

p_{n}(x)
Property / Symbols used: Q11731 / qualifier
 
xml-id: C18.S1.XMD9.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1mdec
Property / Symbols used
 
Property / Symbols used: Q11779 / rank
 
Normal rank
Property / Symbols used: Q11779 / qualifier
 
Defining formula:

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

A(x)
Property / Symbols used: Q11779 / qualifier
 
xml-id: C18.S22.XMD12.m1dec
Property / Symbols used
 
Property / Symbols used: Q11780 / rank
 
Normal rank
Property / Symbols used: Q11780 / qualifier
 
Defining formula:

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

C(x)
Property / Symbols used: Q11780 / qualifier
 
xml-id: C18.S22.XMD13.m1dec

Latest revision as of 01:36, 2 January 2020

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Language Label Description Also known as
English
DLMF:18.22.E14
No description defined

    Statements

    Defining formula
    A ⁢ ( x ) ⁢ p n ⁢ ( x + i ) - ( A ⁢ ( x ) + C ⁢ ( x ) ) ⁢ p n ⁢ ( x ) + C ⁢ ( x ) ⁢ p n ⁢ ( x - i ) + n ⁢ ( n + 2 ⁢ ℜ ⁡ ( a + b ) - 1 ) ⁢ p n ⁢ ( x ) = 0 , 𝐴 𝑥 subscript 𝑝 𝑛 𝑥 𝑖 𝐴 𝑥 𝐶 𝑥 subscript 𝑝 𝑛 𝑥 𝐶 𝑥 subscript 𝑝 𝑛 𝑥 𝑖 𝑛 𝑛 2 𝑎 𝑏 1 subscript 𝑝 𝑛 𝑥 0 {\displaystyle{\displaystyle A(x)p_{n}(x+i)-\left(A(x)+C(x)\right)p_{n}(x)+C(x% )p_{n}(x-i)+n(n+2\Re(a+b)-1)p_{n}(x)=0,}}
    0 references
    DLMF id
    DLMF:18.22.E14
    0 references
    Symbols used
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ndec
    0 references
    Q11731
    Defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1jdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1mdec
    0 references
    Q11779
    Defining formula
    A ⁢ ( x ) 𝐴 𝑥 {\displaystyle{\displaystyle A(x)}}
    xml-id
    C18.S22.XMD12.m1dec
    0 references
    Q11780
    Defining formula
    C ⁢ ( x ) 𝐶 𝑥 {\displaystyle{\displaystyle C(x)}}
    xml-id
    C18.S22.XMD13.m1dec
    0 references
     
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