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

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=-1/4, b_1`>=-11/2

For fixed z and a₁=-1/4, b_1`=3/2

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

Input Form

HypergeometricPFQ[{-(1/4)}, {3/2, 23/4}, z] == (1/(8589934592 z^(19/4))) ((1463 (4 z^(1/4) (6081075 + 8108100 Sqrt[z] + 3991680 z + 380160 z^(3/2) - 207360 z^2 + 153600 z^(5/2) - 196608 z^(7/2) - 65536 z^4 + 262144 z^(9/2) + E^(4 Sqrt[z]) (-6081075 + 8108100 Sqrt[z] - 3991680 z + 380160 z^(3/2) + 207360 z^2 + 153600 z^(5/2) - 196608 z^(7/2) + 65536 z^4 + 262144 z^(9/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-6081075 + 2494800 z - 806400 z^2 + 368640 z^3 - 983040 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-6081075 + 2494800 z - 806400 z^2 + 368640 z^3 - 983040 z^4 + 1048576 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]