DLMF:28.28.E8 (Q8432): Difference between revisions

Latest revision as of 15:19, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:28.28.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\dfrac{1}{\pi}\int_{\mathcal{L}_{j}}2\mathrm{i}h% \frac{\partial w}{\partial\alpha}e^{2\mathrm{i}hw}\mathrm{me}_{\nu}\left(t,h^{% 2}\right)\mathrm{d}t=e^{\mathrm{i}\nu\pi/{2}}\mathrm{me}_{\nu}'\left(\alpha,h^% {2}\right){\mathrm{M}^{(j)}_{\nu}}\left(z,h\right),}}

0 references

DLMF id

DLMF:28.28.E8

0 references

constraint

{\displaystyle{\displaystyle j=3,4}}

0 references

Symbols used

Q12299

Defining formula

{\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}

xml-id

C28.S12.SS2.p2.m2aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

xml-id

C3.S12.E1.m2afdec

0 references

Q10770

Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

xml-id

C1.S4.SS4.m1aedec

0 references

base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

xml-id

C4.S2.E11.m2aedec

0 references

imaginary unit

Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

xml-id

C1.S9.E1.m2afdec

0 references

Q10771

Defining formula

{\displaystyle{\displaystyle\int}}

xml-id

C1.S4.SS4.m3aedec

0 references

Q12301

Defining formula

{\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}

xml-id

C28.S20.SS3.p1.m4aadec

0 references

partial derivative of $$f$$ with respect to $$x$$

Defining formula

{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

xml-id

C1.S5.E3.m4abdec

0 references

partial differential of $$x$$

Defining formula

{\displaystyle{\displaystyle\partial\NVar{x}}}

xml-id

C1.S5.E3.m2abdec

0 references

Q12294

Defining formula

{\displaystyle{\displaystyle h}}

xml-id

C28.S1.XMD11.m1edec

0 references

Q12291

Defining formula

{\displaystyle{\displaystyle j}}

xml-id

C28.S1.XMD3.m1bdec

0 references

Q12272

Defining formula

{\displaystyle{\displaystyle z}}

xml-id

C28.S1.XMD6.m1fdec

0 references

Q12278

Defining formula

{\displaystyle{\displaystyle\nu}}

xml-id

C28.S1.XMD7.m1adec

0 references

Q12274

Defining formula

{\displaystyle{\displaystyle w(z)}}

xml-id

C28.S2.XMD1.m1fdec

0 references

Q12311

Defining formula

{\displaystyle{\displaystyle\alpha}}

xml-id

C28.S28.XMD1.m1fdec

0 references

Q12312

Defining formula

{\displaystyle{\displaystyle\mathcal{L}_{j}}}

xml-id

C28.S28.XMD2.m1bdec

0 references

@@ Property / Symbols used @@
+Q12299
@@ Property / Symbols used: Q12299 / rank @@
+Normal rank
@@ Property / Symbols used: Q12299 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}$ 
\Mathieume{\NVar{n}}@{\NVar{z}}{\NVar{q}}
@@ Property / Symbols used: Q12299 / qualifier @@
+xml-id: C28.S12.SS2.p2.m2aadec
@@ Property / Symbols used @@
+the ratio of the circumference of a circle to its diameter
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle\pi}}$ 
\cpi
+xml-id: C3.S12.E1.m2afdec
@@ Property / Symbols used @@
+Q10770
@@ Property / Symbols used: Q10770 / rank @@
+Normal rank
@@ Property / Symbols used: Q10770 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ 
\diff{\NVar{x}}
@@ Property / Symbols used: Q10770 / qualifier @@
+xml-id: C1.S4.SS4.m1aedec
@@ Property / Symbols used @@
+base of natural logarithm
@@ Property / Symbols used: base of natural logarithm / rank @@
+Normal rank
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{e}}}$ 
\expe
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+xml-id: C4.S2.E11.m2aedec
@@ Property / Symbols used @@
+imaginary unit
@@ Property / Symbols used: imaginary unit / rank @@
+Normal rank
@@ Property / Symbols used: imaginary unit / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{i}}}$ 
\iunit
@@ Property / Symbols used: imaginary unit / qualifier @@
+xml-id: C1.S9.E1.m2afdec
@@ Property / Symbols used @@
+Q10771
@@ Property / Symbols used: Q10771 / rank @@
+Normal rank
@@ Property / Symbols used: Q10771 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\int}}$ 
\int
@@ Property / Symbols used: Q10771 / qualifier @@
+xml-id: C1.S4.SS4.m3aedec
@@ Property / Symbols used @@
+Q12301
@@ Property / Symbols used: Q12301 / rank @@
+Normal rank
@@ Property / Symbols used: Q12301 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}$ 
\modMathieuM{\NVar{j}}{\NVar{\nu}}@{\NVar{z}}{\NVar{h}}
@@ Property / Symbols used: Q12301 / qualifier @@
+xml-id: C28.S20.SS3.p1.m4aadec
@@ Property / Symbols used @@
+partial derivative of $$f$$  with respect to  $$x$$
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$ 
\pderiv{\NVar{f}}{\NVar{x}}
+xml-id: C1.S5.E3.m4abdec
@@ Property / Symbols used @@
+partial differential of $$x$$
@@ Property / Symbols used: partial differential of $$x$$ / rank @@
+Normal rank
@@ Property / Symbols used: partial differential of $$x$$ / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\partial\NVar{x}}}$ 
\pdiff{\NVar{x}}
@@ Property / Symbols used: partial differential of $$x$$ / qualifier @@
+xml-id: C1.S5.E3.m2abdec
@@ Property / Symbols used @@
+Q12294
@@ Property / Symbols used: Q12294 / rank @@
+Normal rank
@@ Property / Symbols used: Q12294 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle h}}$ 
h
@@ Property / Symbols used: Q12294 / qualifier @@
+xml-id: C28.S1.XMD11.m1edec
@@ Property / Symbols used @@
+Q12291
@@ Property / Symbols used: Q12291 / rank @@
+Normal rank
@@ Property / Symbols used: Q12291 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle j}}$ 
j
@@ Property / Symbols used: Q12291 / qualifier @@
+xml-id: C28.S1.XMD3.m1bdec
@@ Property / Symbols used @@
+Q12272
@@ Property / Symbols used: Q12272 / rank @@
+Normal rank
@@ Property / Symbols used: Q12272 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q12272 / qualifier @@
+xml-id: C28.S1.XMD6.m1fdec
@@ Property / Symbols used @@
+Q12278
@@ Property / Symbols used: Q12278 / rank @@
+Normal rank
@@ Property / Symbols used: Q12278 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\nu}}$ 
\nu
@@ Property / Symbols used: Q12278 / qualifier @@
+xml-id: C28.S1.XMD7.m1adec
@@ Property / Symbols used @@
+Q12274
@@ Property / Symbols used: Q12274 / rank @@
+Normal rank
@@ Property / Symbols used: Q12274 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle w(z)}}$ 
w(z)
@@ Property / Symbols used: Q12274 / qualifier @@
+xml-id: C28.S2.XMD1.m1fdec
@@ Property / Symbols used @@
+Q12311
@@ Property / Symbols used: Q12311 / rank @@
+Normal rank
@@ Property / Symbols used: Q12311 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\alpha}}$ 
\alpha
@@ Property / Symbols used: Q12311 / qualifier @@
+xml-id: C28.S28.XMD1.m1fdec
@@ Property / Symbols used @@
+Q12312
@@ Property / Symbols used: Q12312 / rank @@
+Normal rank
@@ Property / Symbols used: Q12312 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathcal{L}_{j}}}$ 
\mathcal{L}_{j}
@@ Property / Symbols used: Q12312 / qualifier @@
+xml-id: C28.S28.XMD2.m1bdec

DLMF:28.28.E8 (Q8432): Difference between revisions

${\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}$

${\displaystyle{\displaystyle\pi}}$

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

${\displaystyle{\displaystyle\mathrm{e}}}$

${\displaystyle{\displaystyle\mathrm{i}}}$

${\displaystyle{\displaystyle\int}}$

${\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}$

${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$

${\displaystyle{\displaystyle\partial\NVar{x}}}$

${\displaystyle{\displaystyle h}}$

${\displaystyle{\displaystyle j}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle\nu}}$

${\displaystyle{\displaystyle w(z)}}$

${\displaystyle{\displaystyle\alpha}}$

${\displaystyle{\displaystyle\mathcal{L}_{j}}}$

Latest revision as of 15:19, 2 January 2020

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DLMF:28.28.E8 (Q8432): Difference between revisions

me n ⁡ ( z , q ) Mathieu-me 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}

π {\displaystyle{\displaystyle\pi}}

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

e {\displaystyle{\displaystyle\mathrm{e}}}

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

∫ {\displaystyle{\displaystyle\int}}

M ν ( j ) ⁡ ( z , h ) modified-Mathieu-M 𝑗 𝜈 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}

∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}

h ℎ {\displaystyle{\displaystyle h}}

j 𝑗 {\displaystyle{\displaystyle j}}

z 𝑧 {\displaystyle{\displaystyle z}}

ν 𝜈 {\displaystyle{\displaystyle\nu}}

w ⁢ ( z ) 𝑤 𝑧 {\displaystyle{\displaystyle w(z)}}

α 𝛼 {\displaystyle{\displaystyle\alpha}}

ℒ j subscript ℒ 𝑗 {\displaystyle{\displaystyle\mathcal{L}_{j}}}

Latest revision as of 15:19, 2 January 2020

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${\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}$

${\displaystyle{\displaystyle\pi}}$

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

${\displaystyle{\displaystyle\mathrm{e}}}$

${\displaystyle{\displaystyle\mathrm{i}}}$

${\displaystyle{\displaystyle\int}}$

${\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}$

${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$

${\displaystyle{\displaystyle\partial\NVar{x}}}$

${\displaystyle{\displaystyle h}}$

${\displaystyle{\displaystyle j}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle\nu}}$

${\displaystyle{\displaystyle w(z)}}$

${\displaystyle{\displaystyle\alpha}}$

${\displaystyle{\displaystyle\mathcal{L}_{j}}}$