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⇑
14
Legendre and Related Functions
⇑
Real Arguments
⇐
14.3
Definitions and Hypergeometric Representations
14.5
Special Values
⇒
§14.4
Graphics
Permalink:
http://dlmf.nist.gov/14.4
Contents
§14.4(i)
Ferrers Functions: 2D Graphs
§14.4(ii)
Ferrers Functions: 3D Surfaces
§14.4(iii)
Associated Legendre Functions: 2D Graphs
§14.4(iv)
Associated Legendre Functions: 3D Surfaces
§14.4(i)
Ferrers Functions: 2D Graphs
Notes:
These graphs were produced at NIST.
Keywords:
Ferrers functions
Permalink:
http://dlmf.nist.gov/14.4.i
Figure 14.4.1:
.
Symbols:
: Ferrers function of the first kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F1
Encodings:
pdf
,
png
Figure 14.4.2:
.
Symbols:
: Ferrers function of the second kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F2
Encodings:
pdf
,
png
Figure 14.4.3:
.
Symbols:
: Ferrers function of the first kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F3
Encodings:
pdf
,
png
Figure 14.4.4:
.
Symbols:
: Ferrers function of the second kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F4
Encodings:
pdf
,
png
Figure 14.4.5:
.
Symbols:
: Ferrers function of the first kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F5
Encodings:
pdf
,
png
Figure 14.4.6:
.
Symbols:
: Ferrers function of the second kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F6
Encodings:
pdf
,
png
Figure 14.4.7:
.
Symbols:
: Ferrers function of the first kind
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F7
Encodings:
pdf
,
png
Figure 14.4.8:
.
Symbols:
: Ferrers function of the second kind
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F8
Encodings:
pdf
,
png
Figure 14.4.9:
.
Symbols:
: Ferrers function of the first kind
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F9
Encodings:
pdf
,
png
Figure 14.4.10:
.
Symbols:
: Ferrers function of the second kind
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F10
Encodings:
pdf
,
png
Figure 14.4.11:
.
Symbols:
: Ferrers function of the first kind
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F11
Encodings:
pdf
,
png
Figure 14.4.12:
.
Symbols:
: Ferrers function of the second kind
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F12
Encodings:
pdf
,
png
§14.4(ii)
Ferrers Functions: 3D Surfaces
Notes:
These surfaces were produced at NIST.
Permalink:
http://dlmf.nist.gov/14.4.ii
Visualization Help
Figure 14.4.13:
.
Symbols:
: Ferrers function of the first kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F13
Encodings:
VRML
,
X3D
,
pdf
,
png
Visualization Help
Figure 14.4.14:
.
Symbols:
: Ferrers function of the second kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F14
Encodings:
VRML
,
X3D
,
pdf
,
png
Visualization Help
Figure 14.4.15:
.
Symbols:
: Ferrers function of the first kind
,
: real variable
and
: general order
Keywords:
Ferrers functions
Permalink:
http://dlmf.nist.gov/14.4.F15
Encodings:
VRML
,
X3D
,
pdf
,
png
Visualization Help
Figure 14.4.16:
.
Symbols:
: Ferrers function of the second kind
,
: real variable
and
: general order
Keywords:
Ferrers functions
Permalink:
http://dlmf.nist.gov/14.4.F16
Encodings:
VRML
,
X3D
,
pdf
,
png
§14.4(iii)
Associated Legendre Functions: 2D Graphs
Notes:
These graphs were produced at NIST.
Keywords:
associated Legendre functions
Permalink:
http://dlmf.nist.gov/14.4.iii
Figure 14.4.17:
.
Symbols:
: associated Legendre function of the first kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F17
Encodings:
pdf
,
png
Figure 14.4.18:
.
Symbols:
: Olver’s associated Legendre function
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F18
Encodings:
pdf
,
png
Figure 14.4.19:
.
Symbols:
: associated Legendre function of the first kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F19
Encodings:
pdf
,
png
Figure 14.4.20:
.
Symbols:
: Olver’s associated Legendre function
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F20
Encodings:
pdf
,
png
Figure 14.4.21:
.
Symbols:
: associated Legendre function of the first kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F21
Encodings:
pdf
,
png
Figure 14.4.22:
.
Symbols:
: Olver’s associated Legendre function
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F22
Encodings:
pdf
,
png
Figure 14.4.23:
.
Symbols:
: associated Legendre function of the first kind
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F23
Encodings:
pdf
,
png
Figure 14.4.24:
.
Symbols:
: Olver’s associated Legendre function
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F24
Encodings:
pdf
,
png
Figure 14.4.25:
.
Symbols:
: associated Legendre function of the first kind
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F25
Encodings:
pdf
,
png
Figure 14.4.26:
.
Symbols:
: Olver’s associated Legendre function
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F26
Encodings:
pdf
,
png
Figure 14.4.27:
.
Symbols:
: associated Legendre function of the first kind
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F27
Encodings:
pdf
,
png
Figure 14.4.28:
.
Symbols:
: Olver’s associated Legendre function
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F28
Encodings:
pdf
,
png
§14.4(iv)
Associated Legendre Functions: 3D Surfaces
Notes:
These surfaces were produced at NIST.
Keywords:
associated Legendre functions
Permalink:
http://dlmf.nist.gov/14.4.iv
Visualization Help
Figure 14.4.29:
.
Symbols:
: associated Legendre function of the first kind
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F29
Encodings:
VRML
,
X3D
,
pdf
,
png
Visualization Help
Figure 14.4.30:
.
Symbols:
: Olver’s associated Legendre function
,
: real variable
and
: general degree
Permalink:
http://dlmf.nist.gov/14.4.F30
Encodings:
VRML
,
X3D
,
pdf
,
png
Visualization Help
Figure 14.4.31:
.
Symbols:
: associated Legendre function of the first kind
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F31
Encodings:
VRML
,
X3D
,
pdf
,
png
Visualization Help
Figure 14.4.32:
.
Symbols:
: Olver’s associated Legendre function
,
: real variable
and
: general order
Permalink:
http://dlmf.nist.gov/14.4.F32
Encodings:
VRML
,
X3D
,
pdf
,
png
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