Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aely)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.aely.01

Input Form

HypergeometricPFQ[{15/4}, {-(11/2), 23/4}, z] == (1/(372051542016 z^(19/4))) ((19 (4 z^(1/4) (26264240610733125 + 35018987480977500 Sqrt[z] + 27331892668080000 z + 15097616902368000 z^(3/2) + 6386118413875200 z^2 + 2170775429222400 z^(5/2) + 610975553126400 z^3 + 144977249894400 z^(7/2) + 29239109222400 z^4 + 4995324837888 z^(9/2) + 708392779776 z^5 + 79373008896 z^(11/2) + 6308233216 z^6 + 268435456 z^(13/2) + E^(4 Sqrt[z]) (-26264240610733125 + 35018987480977500 Sqrt[z] - 27331892668080000 z + 15097616902368000 z^(3/2) - 6386118413875200 z^2 + 2170775429222400 z^(5/2) - 610975553126400 z^3 + 144977249894400 z^(7/2) - 29239109222400 z^4 + 4995324837888 z^(9/2) - 708392779776 z^5 + 79373008896 z^(11/2) - 6308233216 z^6 + 268435456 z^(13/2))) + 42706082293875 E^(2 Sqrt[z]) Sqrt[2 Pi] (-615 + 16 z) Erf[Sqrt[2] z^(1/4)] - 42706082293875 E^(2 Sqrt[z]) Sqrt[2 Pi] (-615 + 16 z) Erfi[Sqrt[2] z^(1/4)]))/E^(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]