Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7370)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-23/4

http://functions.wolfram.com/07.22.03.7370.01

Input Form

HypergeometricPFQ[{5}, {-(23/4), -(13/4)}, z] == (1/2657429775) ((E^(2 Sqrt[z]) (2657429775 + 711018000 z + 199584000 z^2 + 99348480 z^3 + 289013760 z^4 + 118121472 z^5 + 45998080 z^6 + 131072 z^7) + 64 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (1507275 - 3014550 Sqrt[z] + 1244100 z + 1531200 z^(3/2) + 367488 z^2 + 33280 z^(5/2) + 1024 z^3) Erf[Sqrt[2] z^(1/4)] - 64 Sqrt[2 Pi] z^(17/4) (1507275 + 3014550 Sqrt[z] + 1244100 z - 1531200 z^(3/2) + 367488 z^2 - 33280 z^(5/2) + 1024 z^3) 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]