Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8bq)

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`=11/2

http://functions.wolfram.com/07.22.03.a8bq.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, -(11/4)}, z] == (1/(1250708659200 z^(9/2))) ((-55087698290625 + 55087698290625 E^(4 Sqrt[z]) - 110175396581250 Sqrt[z] - 110175396581250 E^(4 Sqrt[z]) Sqrt[z] - 92265110437500 z + 92265110437500 E^(4 Sqrt[z]) z - 37629692100000 z^(3/2) - 37629692100000 E^(4 Sqrt[z]) z^(3/2) - 5059746291600 z^2 + 5059746291600 E^(4 Sqrt[z]) z^2 + 879955876800 z^(5/2) + 879955876800 E^(4 Sqrt[z]) z^(5/2) - 167610643200 z^3 + 167610643200 E^(4 Sqrt[z]) z^3 + 35286451200 z^(7/2) + 35286451200 E^(4 Sqrt[z]) z^(7/2) - 8302694400 z^4 + 8302694400 E^(4 Sqrt[z]) z^4 + 2214051840 z^(9/2) + 2214051840 E^(4 Sqrt[z]) z^(9/2) - 681246720 z^5 + 681246720 E^(4 Sqrt[z]) z^5 + 247726080 z^(11/2) + 247726080 E^(4 Sqrt[z]) z^(11/2) - 110100480 z^6 + 110100480 E^(4 Sqrt[z]) z^6 + 62914560 z^(13/2) + 62914560 E^(4 Sqrt[z]) z^(13/2) - 50331648 z^7 + 50331648 E^(4 Sqrt[z]) z^7 + 67108864 z^(15/2) + 67108864 E^(4 Sqrt[z]) z^(15/2) - 268435456 z^8 + 268435456 E^(4 Sqrt[z]) z^8 - 268435456 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) Erf[Sqrt[2] z^(1/4)] - 268435456 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) 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]