Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8936)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8936.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 7/4}, z] == (-4 (76988620800 + 153977241600 Sqrt[z] + 1465255475775 z - 8774103926700 z^(3/2) - 1554829350480 z^2 + 6906725340480 z^(5/2) + 268385564160 z^3 - 1111606917120 z^(7/2) - 13415915520 z^4 + 54318759936 z^(9/2) + 221970432 z^5 - 891027456 z^(11/2) - 1048576 z^6 + 4194304 z^(13/2) + E^(4 Sqrt[z]) (-76988620800 + 153977241600 Sqrt[z] - 1465255475775 z - 8774103926700 z^(3/2) + 1554829350480 z^2 + 6906725340480 z^(5/2) - 268385564160 z^3 - 1111606917120 z^(7/2) + 13415915520 z^4 + 54318759936 z^(9/2) - 221970432 z^5 - 891027456 z^(11/2) + 1048576 z^6 + 4194304 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (-2846107289025 + 39032328535200 z - 28387148025600 z^2 + 4485870305280 z^3 - 217937018880 z^4 + 3567255552 z^5 - 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (2846107289025 - 39032328535200 z + 28387148025600 z^2 - 4485870305280 z^3 + 217937018880 z^4 - 3567255552 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(107173733990400 z^(3/2))

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]