Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1242)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=3/2

http://functions.wolfram.com/07.22.03.1242.01

Input Form

HypergeometricPFQ[{-(7/2)}, {3/2, 4}, -z] == (1/(2162160 z^(5/2))) (4 (2 Sqrt[z] (7560 + 12600 z + 352800 z^2 + 569523 z^3 + 121564 z^4 + 5840 z^5 + 64 z^6) BesselJ[0, 2 Sqrt[z]] - (15120 + 17640 z + 151200 z^2 + 513561 z^3 + 118700 z^4 + 5808 z^5 + 64 z^6) BesselJ[1, 2 Sqrt[z]]) + Pi z^(5/2) (945945 + 2162160 z + 480480 z^2 + 23296 z^3 + 256 z^4) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi z^(5/2) (945945 + 2162160 z + 480480 z^2 + 23296 z^3 + 256 z^4) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

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)

2007-05-02

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]