Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8122)

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`=-5/2

http://functions.wolfram.com/07.22.03.8122.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 9/4}, z] == (4 z^(1/4) (236102414625 + 314803219500 Sqrt[z] - 84153232800 z + 647183779200 z^(3/2) - 68264259840 z^2 + 349534725120 z^(5/2) - 21970206720 z^3 + 151174840320 z^(7/2) + 25701580800 z^4 - 107144282112 z^(9/2) - 1503657984 z^5 + 6064963584 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (236102414625 - 314803219500 Sqrt[z] - 84153232800 z - 647183779200 z^(3/2) - 68264259840 z^2 - 349534725120 z^(5/2) - 21970206720 z^3 - 151174840320 z^(7/2) + 25701580800 z^4 + 107144282112 z^(9/2) - 1503657984 z^5 - 6064963584 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (236102414625 - 1762898029200 z - 2564215315200 z^2 - 1395491328000 z^3 - 676601856000 z^4 + 433025187840 z^5 - 24310185984 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (236102414625 - 1762898029200 z - 2564215315200 z^2 - 1395491328000 z^3 - 676601856000 z^4 + 433025187840 z^5 - 24310185984 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(11415217766400 z^(5/4))

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]