Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8194)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.8194.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), -(15/4)}, z] == (1/68918850) ((34459425 + 34459425 E^(4 Sqrt[z]) + 68918850 Sqrt[z] - 68918850 E^(4 Sqrt[z]) Sqrt[z] - 36756720 z - 36756720 E^(4 Sqrt[z]) z + 16299360 z^(3/2) - 16299360 E^(4 Sqrt[z]) z^(3/2) - 7499520 z^2 - 7499520 E^(4 Sqrt[z]) z^2 + 3924480 z^(5/2) - 3924480 E^(4 Sqrt[z]) z^(5/2) - 2519040 z^3 - 2519040 E^(4 Sqrt[z]) z^3 + 2187264 z^(7/2) - 2187264 E^(4 Sqrt[z]) z^(7/2) - 3080192 z^4 - 3080192 E^(4 Sqrt[z]) z^4 + 12713984 z^(9/2) - 12713984 E^(4 Sqrt[z]) z^(9/2) + 131072 z^5 + 131072 E^(4 Sqrt[z]) z^5 - 524288 z^(11/2) + 524288 E^(4 Sqrt[z]) z^(11/2) - 32768 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (-391 + 16 z) Erf[Sqrt[2] z^(1/4)] - 32768 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (-391 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML 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]