DLMF:4.25.E2 (Q1813): Difference between revisions

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Property / constraint
 

| ℜ ⁡ z | < 1 2 ⁢ π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\Re z|<\tfrac{1}{2}\pi}}

|\Re z|<\tfrac{1}{2}\pi
Property / constraint: | ℜ ⁡ z | < 1 2 ⁢ π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\Re z|<\tfrac{1}{2}\pi}} / rank
 
Normal rank
Property / constraint
 

a ⁢ z ≠ ± 1 2 ⁢ π , ± 3 2 ⁢ π , … 𝑎 𝑧 plus-or-minus 1 2 𝜋 plus-or-minus 3 2 𝜋 … {\displaystyle{\displaystyle az\neq\pm\tfrac{1}{2}\pi,\pm\tfrac{3}{2}\pi,\dots}}

az\neq\pm\tfrac{1}{2}\pi,\pm\tfrac{3}{2}\pi,\dots
Property / constraint: a ⁢ z ≠ ± 1 2 ⁢ π , ± 3 2 ⁢ π , … 𝑎 𝑧 plus-or-minus 1 2 𝜋 plus-or-minus 3 2 𝜋 … {\displaystyle{\displaystyle az\neq\pm\tfrac{1}{2}\pi,\pm\tfrac{3}{2}\pi,\dots}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

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

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
test:

tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11221 / rank
 
Normal rank
Property / Symbols used: Q11221 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11221 / qualifier
 
xml-id: C4.S1.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1adec

Latest revision as of 17:39, 1 January 2020

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DLMF:4.25.E2
No description defined

    Statements

    test
    tan ⁡ ( a ⁢ z ) = a ⁢ tan ⁡ z 1 + ( 1 - a 2 ) ⁢ tan 2 ⁡ z 3 + ( 4 - a 2 ) ⁢ tan 2 ⁡ z 5 + ( 9 - a 2 ) ⁢ tan 2 ⁡ z 7 + ⁢ ⋯ , 𝑎 𝑧 continued-fraction 𝑎 𝑧 1 continued-fraction 1 superscript 𝑎 2 2 𝑧 3 continued-fraction 4 superscript 𝑎 2 2 𝑧 5 continued-fraction 9 superscript 𝑎 2 2 𝑧 limit-from 7 ⋯ {\displaystyle{\displaystyle\tan\left(az\right)=\cfrac{a\tan z}{1+\cfrac{(1-a^% {2}){\tan^{2}}z}{3+\cfrac{(4-a^{2}){\tan^{2}}z}{5+\cfrac{(9-a^{2}){\tan^{2}}z}% {7+}}}}\cdots,}}
    0 references
    DLMF id
    DLMF:4.25.E2
    0 references
    constraint
    | ℜ ⁡ z | < 1 2 ⁢ π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\Re z|<\tfrac{1}{2}\pi}}
    0 references
    | ℜ ⁡ z | < 1 2 ⁢ π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\Re z|<\tfrac{1}{2}\pi}}
    0 references
    a ⁢ z ≠ ± 1 2 ⁢ π , ± 3 2 ⁢ π , … 𝑎 𝑧 plus-or-minus 1 2 𝜋 plus-or-minus 3 2 𝜋 … {\displaystyle{\displaystyle az\neq\pm\tfrac{1}{2}\pi,\pm\tfrac{3}{2}\pi,\dots}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    tangent function
    test
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2aadec
    0 references
    Q11221
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1dec
    0 references
    Q11217
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1adec
    0 references
     
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