§11.3 Graphics

Permalink:: http://dlmf.nist.gov/11.3

§11.3(i) Struve Functions
§11.3(ii) Modified Struve Functions

§11.3(i) Struve Functions

Notes:: These graphics were produced at NIST.
Permalink:: http://dlmf.nist.gov/11.3.i

Figure 11.3.1: $\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0\leq x\leq 12$ and $\nu=0,\frac{1}{2},1,\frac{3}{2},2,3$ .

Symbols:: $\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F1
Encodings:: pdf, png

Figure 11.3.2: $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0<x\leq 16$ and $\nu=0,\frac{1}{2},1,\frac{3}{2},2,3$ .

Symbols:: $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F2
Encodings:: pdf, png

Figure 11.3.3: $\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0\leq x\leq 12$ and $\nu=-3,-2,-\frac{3}{2},-1,-\frac{1}{2}$ .

Symbols:: $\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F3
Encodings:: pdf, png

Figure 11.3.4: $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0<x\leq 16$ and $\nu=-4,-3,-2,-1,0$ . If $\nu=-\frac{1}{2},-\frac{3}{2}$ , …, then $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(x\right)$ is identically zero.

Symbols:: $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F4
Encodings:: pdf, png

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Figure 11.3.5: $\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0\leq x\leq 8$ and $-4\leq\nu\leq 4$ .

Symbols:: $\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F5
Encodings:: VRML, X3D, pdf, png

Visualization Help

Figure 11.3.6: $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0\leq x\leq 8$ and $-4\leq\nu\leq 4$ .

Symbols:: $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F6
Encodings:: VRML, X3D, pdf, png

Visualization Help

Figure 11.3.7: $\left|\mathop{\mathbf{H}_{{0}}\/}\nolimits\!\left(x+iy\right)\right|$ for $-8\leq x\leq 8$ and $-3\leq y\leq 3$ .

Symbols:: $\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function and $x$ : real variable
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F7
Encodings:: VRML, X3D, pdf, png

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Figure 11.3.8: $\left|\mathop{\mathbf{K}_{{0}}\/}\nolimits\!\left(x+iy\right)\right|$ (principal value) for $-8\leq x\leq 8$ and $-3\leq y\leq 3$ . There is a cut along the negative real axis.

Symbols:: $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function and $x$ : real variable
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F8
Encodings:: VRML, X3D, pdf, png

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Figure 11.3.9: $|\mathop{\mathbf{H}_{{\frac{1}{2}}}\/}\nolimits\!\left(x+iy\right)|$ (principal value) for $-8\leq x\leq 8$ and $-3\leq y\leq 3$ . There is a cut along the negative real axis.

Symbols:: $\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function and $x$ : real variable
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F9
Encodings:: VRML, X3D, pdf, png

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Figure 11.3.10: $|\mathop{\mathbf{K}_{{\frac{1}{2}}}\/}\nolimits\!\left(x+iy\right)|$ (principal value) for $-8\leq x\leq 8$ and $-3\leq y\leq 3$ . There is a cut along the negative real axis.

Symbols:: $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function and $x$ : real variable
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F10
Encodings:: VRML, X3D, pdf, png

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Figure 11.3.11: $\left|\mathop{\mathbf{H}_{{1}}\/}\nolimits\!\left(x+iy\right)\right|$ for $-8.5\leq x\leq 8.5$ and $-3\leq y\leq 3$ .

Symbols:: $\mathop{\mathbf{H}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function and $x$ : real variable
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F11
Encodings:: VRML, X3D, pdf, png

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Figure 11.3.12: $\left|\mathop{\mathbf{K}_{{1}}\/}\nolimits\!\left(x+iy\right)\right|$ (principal value) for $-8\leq x\leq 8$ and $-3\leq y\leq 3$ . There is a cut along the negative real axis.

Symbols:: $\mathop{\mathbf{K}_{{\nu}}\/}\nolimits\!\left(z\right)$ : Struve function and $x$ : real variable
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F12
Encodings:: VRML, X3D, pdf, png

§11.3(ii) Modified Struve Functions

Notes:: These graphics were produced at NIST.
Permalink:: http://dlmf.nist.gov/11.3.ii

Figure 11.3.13: $\mathop{\mathbf{L}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0\leq x<4.38$ and $\nu=0,\frac{1}{2},1,\frac{3}{2},2,3$ .

Symbols:: $\mathop{\mathbf{L}_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F13
Encodings:: pdf, png

Figure 11.3.14: $\mathop{\mathbf{M}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0\leq x\leq 16$ and $\nu=0,\frac{1}{2},1,\frac{3}{2},2,3$ .

Symbols:: $\mathop{\mathbf{M}_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F14
Encodings:: pdf, png

Figure 11.3.15: $\mathop{\mathbf{L}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0\leq x<4.25$ and $\nu=-3,-2,-\frac{3}{2},-1,-\frac{1}{2}$ .

Symbols:: $\mathop{\mathbf{L}_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F15
Encodings:: pdf, png

Figure 11.3.16: $\mathop{\mathbf{M}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0<x\leq 16$ and $\nu=-3,-2,-\frac{3}{2},-1,-\frac{1}{2}$ .

Symbols:: $\mathop{\mathbf{M}_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F16
Encodings:: pdf, png

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Figure 11.3.17: $\mathop{\mathbf{L}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0\leq x\leq 5.6$ and $-4\leq\nu\leq 4$ .

Symbols:: $\mathop{\mathbf{L}_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F17
Encodings:: VRML, X3D, pdf, png

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Figure 11.3.18: $\mathop{\mathbf{M}_{{\nu}}\/}\nolimits\!\left(x\right)$ for $0\leq x\leq 8$ and $-4\leq\nu\leq 4$ .

Symbols:: $\mathop{\mathbf{M}_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Struve function, $x$ : real variable and $\nu$ : real or complex order
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F18
Encodings:: VRML, X3D, pdf, png

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Figure 11.3.19: $|\mathop{\mathbf{M}_{{-\frac{1}{2}}}\/}\nolimits\!\left(x+iy\right)|$ (principal value) for $-3\leq x\leq 3$ and $-3\leq y\leq 3$ . There is a cut along the negative real axis.

Symbols:: $\mathop{\mathbf{M}_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Struve function and $x$ : real variable
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F19
Encodings:: VRML, X3D, pdf, png

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Figure 11.3.20: $|\mathop{\mathbf{M}_{{\frac{1}{2}}}\/}\nolimits\!\left(x+iy\right)|$ (principal value) for $-3\leq x\leq 3$ and $-3\leq y\leq 3$ . There is a cut along the negative real axis.

Symbols:: $\mathop{\mathbf{M}_{{\nu}}\/}\nolimits\!\left(z\right)$ : modified Struve function and $x$ : real variable
Keywords:: Struve functions and modified Struve functions
Permalink:: http://dlmf.nist.gov/11.3.F20
Encodings:: VRML, X3D, pdf, png

§11.3 Graphics

Contents

§11.3(i) Struve Functions

§11.3(ii) Modified Struve Functions