Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7666)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-23/4

http://functions.wolfram.com/07.22.03.7666.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), -(1/4)}, z] == (1/726818400) ((-16 E^(2 Sqrt[z]) (-45426150 - 189604800 z - 142652475 z^2 + 65856420 z^3 - 7558320 z^4 + 1248768 z^5 + 4096 z^6) + E^(4 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (986792625 - 1973585250 Sqrt[z] + 1266993000 z + 97461000 z^(3/2) - 499086000 z^2 + 166504800 z^(5/2) + 54768000 z^3 - 29568000 z^(7/2) - 10240000 z^4 - 1024000 z^(9/2) - 32768 z^5) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] z^(5/4) (-986792625 - 1973585250 Sqrt[z] - 1266993000 z + 97461000 z^(3/2) + 499086000 z^2 + 166504800 z^(5/2) - 54768000 z^3 - 29568000 z^(7/2) + 10240000 z^4 - 1024000 z^(9/2) + 32768 z^5) 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]