Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0303)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

Specialized values

For fixed a₁, b₂, z

http://functions.wolfram.com/07.22.03.0303.01

Input Form

HypergeometricPFQ[{a}, {a - 5, c}, z] == z^((1 - c)/2) (((-z) (-10 a^3 + 11 c^2 + c^3 + 10 a^2 (7 + c) - 5 a (30 + 9 c + c^2) + 2 c (23 + z) + 4 (24 + z)) + (-1 + a) (-154 a + 71 a^2 - 14 a^3 + a^4 + 5 (24 + z^2))) BesselI[-1 + c, 2 Sqrt[z]] + Sqrt[z] (120 + 5 a^4 + 11 c^3 + c^4 - 10 a^3 (5 + c) + 36 z + z^2 + 5 a^2 (35 + 14 c + 2 c^2 + 2 z) + c^2 (46 + 3 z) + c (96 + 19 z) - 5 a (50 + 9 c^2 + c^3 + 8 z + 2 c (15 + z))) BesselI[c, 2 Sqrt[z]]) (Gamma[c]/((-5 + a) (-4 + a) (-3 + a) (-2 + a) (-1 + a)))

Standard Form

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MathML Form

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</apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <ci> c </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2002-12-18

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]