Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8b6)

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`=9/2

http://functions.wolfram.com/07.22.03.a8b6.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, 17/4}, z] == (-4 (-8583708672000 + 6441596209125 Sqrt[z] - 18879072804900 z + 6117534007200 z^(3/2) - 18878258044800 z^2 + 6183391737600 z^(5/2) - 30491379072000 z^3 - 2377855549440 z^(7/2) + 9965462814720 z^4 + 161703198720 z^(9/2) - 656171335680 z^5 - 3177185280 z^(11/2) + 12759072768 z^6 + 16777216 z^(13/2) - 67108864 z^7 + E^(4 Sqrt[z]) (8583708672000 + 6441596209125 Sqrt[z] + 18879072804900 z + 6117534007200 z^(3/2) + 18878258044800 z^2 + 6183391737600 z^(5/2) + 30491379072000 z^3 - 2377855549440 z^(7/2) - 9965462814720 z^4 + 161703198720 z^(9/2) + 656171335680 z^5 - 3177185280 z^(11/2) - 12759072768 z^6 + 16777216 z^(13/2) + 67108864 z^7)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (23609013553125 + 58760211510000 z + 62677558944000 z^2 + 128569351680000 z^3 - 40335482880000 z^4 + 2634153984000 z^5 - 51086622720 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (23609013553125 + 58760211510000 z + 62677558944000 z^2 + 128569351680000 z^3 - 40335482880000 z^4 + 2634153984000 z^5 - 51086622720 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(416866841395200 z^(7/2))

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]