Generalized hypergeometric function 1F2: Differentiation (formula 07.22.20.0011)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Differentiation

Low-order differentiation

With respect to element of parameters ||| With respect to element of parameters

http://functions.wolfram.com/07.22.20.0011.01

Input Form

(D[HypergeometricPFQ[{1}, {b, b + n}, z], b] /. b -> 1) == ((n - 1)! (BesselI[n, 2 Sqrt[z]] (1 - EulerGamma n - n Log[z] + n PolyGamma[n]) + (-1)^(n - 1) n (2 BesselK[n, 2 Sqrt[z]] - Sum[(((-1)^k (n - k - 1)!)/k!) z^(k - n/2), {k, 0, n - 1}])))/ z^(n/2) /; Element[n, Integers] && n > 0

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]