partial derivative
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11—20 of 59 matching pages
11: 1.6 Vectors and Vector-Valued Functions
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βΊ
1.6.19
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βΊ
β
- Symbols:
- : partial derivative of with respect to , : partial differential of , : variable, : unit vector, : unit vector and : unit vector
- Permalink:
- http://dlmf.nist.gov/1.6.E19
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1
1.6.20
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βΊ
β
- Defines:
- : gradient of differentiable scalar function
- Symbols:
- : partial derivative of with respect to , : partial differential of , : variable, : unit vector, : unit vector and : unit vector
- Permalink:
- http://dlmf.nist.gov/1.6.E20
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1
1.6.22
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βΊ
β
- Defines:
- : of vector-valued function
- Symbols:
- : determinant, : partial derivative of with respect to , : partial differential of , : variable, : unit vector, : unit vector, : unit vector and : vector function components
- Permalink:
- http://dlmf.nist.gov/1.6.E22
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1
1.6.46
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βΊwhere is the derivative of normal to the surface outwards from and is the unit outer normal vector.
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β
- Symbols:
- : open interval, : partial derivative of with respect to , : partial differential of , : unit vector, : unit vector and : unit vector
- Permalink:
- http://dlmf.nist.gov/1.6.E46
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §1.6(v), §1.6 and Ch.1
12: 23.21 Physical Applications
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βΊ
23.21.2
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βΊ
β
- Symbols:
- : partial derivative of with respect to , : partial differential of , : ellipsoidal coordinate, : ellipsoidal coordinate, : ellipsoidal coordinate and : function
- Permalink:
- http://dlmf.nist.gov/23.21.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §23.21(iii), §23.21 and Ch.23
23.21.5
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β
- Symbols:
- (= = ): Weierstrass -function, : partial derivative of with respect to , : partial differential of , : lattice, : change of variable, : change of variable and : change of variable
- Permalink:
- http://dlmf.nist.gov/23.21.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §23.21(iii), §23.21 and Ch.23
13: 28.32 Mathematical Applications
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βΊ
28.32.2
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βΊ
β
- Symbols:
- : partial derivative of with respect to , : partial differential of , : real variable, : real variable, : parameter and : solution
- Referenced by:
- §28.33(ii)
- Permalink:
- http://dlmf.nist.gov/28.32.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.32(i), §28.32 and Ch.28
28.32.3
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βΊ
β
- Symbols:
- : cosine function, : hyperbolic cosine function, : partial derivative of with respect to , : partial differential of , : variable, : variable, : parameter and : solution
- Referenced by:
- §28.32(i), §28.33(ii)
- Permalink:
- http://dlmf.nist.gov/28.32.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.32(i), §28.32 and Ch.28
28.32.4
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βΊ
β
- Symbols:
- : cosine function, : partial derivative of with respect to , : partial differential of , : parameter, : complex variable, : variable and : solution
- Permalink:
- http://dlmf.nist.gov/28.32.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.32(i), §28.32 and Ch.28
28.32.5
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β
- Symbols:
- : derivative of with respect to , : partial derivative of with respect to , : partial differential of , : complex variable, : variable, : solution and : solution
- Permalink:
- http://dlmf.nist.gov/28.32.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §28.32(i), §28.32 and Ch.28
14: 31.10 Integral Equations and Representations
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βΊ
31.10.4
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βΊ
β
- Defines:
- : Heun’s operator (locally)
- Symbols:
- : partial derivative of with respect to , : partial differential of , : complex variable, : real or complex parameter, : real or complex parameter, : real or complex parameter, : complex parameter, : real or complex parameter and : real or complex parameter
- Referenced by:
- §31.10(ii)
- Permalink:
- http://dlmf.nist.gov/31.10.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §31.10(i), §31.10 and Ch.31
31.10.5
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βΊ
β
- Symbols:
- : derivative of with respect to , : partial derivative of with respect to , : partial differential of , : contour and : kernel
- Permalink:
- http://dlmf.nist.gov/31.10.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §31.10(i), §31.10 and Ch.31
31.10.8
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βΊ
β
- Symbols:
- : cotangent function, : partial derivative of with respect to , : partial differential of , : sine function, : tangent function, : real or complex parameter, : real or complex parameter, : real or complex parameter, : real or complex parameter, : real or complex parameter, : kernel, : angle and : angle
- Referenced by:
- §31.10(i)
- Permalink:
- http://dlmf.nist.gov/31.10.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §31.10(i), §31.10(i), §31.10 and Ch.31
31.10.18
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βΊ
β
- Symbols:
- : partial derivative of with respect to , : partial differential of , : real or complex parameter, : real or complex parameter, : real or complex parameter, : kernel, , and
- Permalink:
- http://dlmf.nist.gov/31.10.E18
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §31.10(ii), §31.10(ii), §31.10 and Ch.31
31.10.21
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β
- Symbols:
- : cotangent function, : partial derivative of with respect to , : partial differential of , : sine function, : tangent function, : real or complex parameter, : real or complex parameter, : real or complex parameter, : kernel, : radius, : angle and : angle
- Permalink:
- http://dlmf.nist.gov/31.10.E21
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §31.10(ii), §31.10(ii), §31.10 and Ch.31
15: 36.4 Bifurcation Sets
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βΊ
βΊ
…
βΊ
36.4.1
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βΊ
β
- Symbols:
- : cuspoid catastrophe of codimension , : partial derivative of with respect to , : partial differential of , : variable, : codimension and : solutions
- Referenced by:
- §36.11, §36.12(i), §36.4(i), §36.5(i), §36.5(ii)
- Permalink:
- http://dlmf.nist.gov/36.4.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §36.4(i), §36.4(i), §36.4 and Ch.36
36.4.3
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βΊ
β
- Symbols:
- : cuspoid catastrophe of codimension , : partial derivative of with respect to , : partial differential of , : variable and : codimension
- Permalink:
- http://dlmf.nist.gov/36.4.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §36.4(i), §36.4(i), §36.4 and Ch.36
36.4.4
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β
- Symbols:
- : partial derivative of with respect to , : partial differential of , : elliptic umbilic catastrophe for , : variable and : variable
- Permalink:
- http://dlmf.nist.gov/36.4.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §36.4(i), §36.4(i), §36.4 and Ch.36
16: 36.12 Uniform Approximation of Integrals
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βΊAlso, is real analytic, and for all such that all critical points coincide.
If , then we may evaluate the complex conjugate of for real values of and , and obtain by conjugation and analytic continuation.
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βΊ
…
36.12.2
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βΊ
β
- Symbols:
- : partial derivative of with respect to , : partial differential of , : function and : mapping
- Permalink:
- http://dlmf.nist.gov/36.12.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §36.12(i), §36.12 and Ch.36
36.12.10
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βΊ
β
- Symbols:
- : cuspoid catastrophe of codimension , : partial derivative of with respect to , : partial differential of , : integer, : variable, : codimension, : function, : function, : mapping, : function and : solutions
- Referenced by:
- §36.12(i)
- Permalink:
- http://dlmf.nist.gov/36.12.E10
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §36.12(i), §36.12 and Ch.36
17: 19.4 Derivatives and Differential Equations
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βΊ
19.4.4
βΊ
β
- Symbols:
- : Legendre’s complete elliptic integral of the second kind, : Legendre’s complete elliptic integral of the third kind, : partial derivative of with respect to , : partial differential of , : real or complex modulus, : complementary modulus and : real or complex parameter
- Permalink:
- http://dlmf.nist.gov/19.4.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §19.4(i), §19.4 and Ch.19
19.4.5
βΊ
β
- Symbols:
- : cosine function, : Legendre’s incomplete elliptic integral of the first kind, : Legendre’s incomplete elliptic integral of the second kind, : partial derivative of with respect to , : partial differential of , : sine function, : real or complex argument, : real or complex modulus and : complementary modulus
- Permalink:
- http://dlmf.nist.gov/19.4.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §19.4(i), §19.4 and Ch.19
19.4.6
βΊ
β
- Symbols:
- : Legendre’s incomplete elliptic integral of the first kind, : Legendre’s incomplete elliptic integral of the second kind, : partial derivative of with respect to , : partial differential of , : real or complex argument and : real or complex modulus
- Referenced by:
- §19.30(i)
- Permalink:
- http://dlmf.nist.gov/19.4.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §19.4(i), §19.4 and Ch.19
19.4.7
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βΊLet .
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β
- Symbols:
- : cosine function, : Legendre’s incomplete elliptic integral of the second kind, : Legendre’s incomplete elliptic integral of the third kind, : partial derivative of with respect to , : partial differential of , : sine function, : real or complex argument, : real or complex modulus, : complementary modulus and : real or complex parameter
- Permalink:
- http://dlmf.nist.gov/19.4.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §19.4(i), §19.4 and Ch.19
18: 14.11 Derivatives with Respect to Degree or Order
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βΊ
14.11.1
βΊ
β
- Symbols:
- : Ferrers function of the first kind, : the ratio of the circumference of a circle to its diameter, : cotangent function, : partial derivative of with respect to , : partial differential of , : real variable, : general order, : general degree and
- Referenced by:
- §14.11, §14.11
- Permalink:
- http://dlmf.nist.gov/14.11.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.11 and Ch.14
14.11.2
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βΊ
β
- Symbols:
- : Ferrers function of the first kind, : Ferrers function of the second kind, : the ratio of the circumference of a circle to its diameter, : cosecant function, : cotangent function, : partial derivative of with respect to , : partial differential of , : sine function, : real variable, : general order, : general degree and
- Referenced by:
- §14.11
- Permalink:
- http://dlmf.nist.gov/14.11.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.11 and Ch.14
14.11.4
βΊ
β
- Symbols:
- : Ferrers function of the first kind, : the ratio of the circumference of a circle to its diameter, : cotangent function, : psi (or digamma) function, : partial derivative of with respect to , : partial differential of , : Ferrers function of the first kind, : Ferrers function of the second kind, : real variable, : general order and : general degree
- Referenced by:
- §14.11, §14.11
- Permalink:
- http://dlmf.nist.gov/14.11.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.11 and Ch.14
14.11.5
…
β
- Symbols:
- : Ferrers function of the second kind, : the ratio of the circumference of a circle to its diameter, : cotangent function, : psi (or digamma) function, : partial derivative of with respect to , : partial differential of , : Ferrers function of the first kind, : Ferrers function of the second kind, : real variable, : general order and : general degree
- Referenced by:
- §14.11
- Permalink:
- http://dlmf.nist.gov/14.11.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §14.11 and Ch.14
19: 3.4 Differentiation
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βΊ
§3.4(iii) Partial Derivatives
… βΊ
3.4.21
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βΊ
β
- Symbols:
- : order not exceeding, : partial derivative of with respect to , : partial differential of and : function
- A&S Ref:
- 25.3.22
- Permalink:
- http://dlmf.nist.gov/3.4.E21
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §3.4(iii), §3.4(iii), §3.4 and Ch.3
3.4.22
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βΊ
β
- Symbols:
- : order not exceeding, : partial derivative of with respect to , : partial differential of and : function
- A&S Ref:
- 25.3.23
- Permalink:
- http://dlmf.nist.gov/3.4.E22
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §3.4(iii), §3.4(iii), §3.4 and Ch.3
3.4.27
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βΊ
β
- Symbols:
- : partial derivative of with respect to , : partial differential of and : function
- A&S Ref:
- 25.3.30
- Permalink:
- http://dlmf.nist.gov/3.4.E27
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §3.4(iii), §3.4(iii), §3.4 and Ch.3
20: 32.4 Isomonodromy Problems
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βΊ
βΊ
…
βΊ
32.4.3
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β
- Symbols:
- : partial derivative of with respect to , : partial differential of and : real
- Referenced by:
- §32.4(i)
- Permalink:
- http://dlmf.nist.gov/32.4.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §32.4(i), §32.4 and Ch.32