Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1417)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, a₂>=-11/2

For fixed z and a₁=-11/2, a₂=2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=2, b₁=11/2

http://functions.wolfram.com/07.25.03.1417.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {11/2, 6}, -z] == (12 (120 + 1890 z + 3990 z^2 + 2261 z^3))/(4199 z^5) + (1/(43341742080 z^5)) ((-14863564800 - 152719536375 z - 213272655750 z^2 - 67614901200 z^3 + 18443224800 z^4 + 14528273760 z^5 + 3250752960 z^6 + 354743040 z^7 + 20393472 z^8 + 588032 z^9 + 6656 z^10)/E^z) + (1/(86683484160 z^(9/2))) (Sqrt[Pi] (-96245174025 - 458310352500 z - 494975180700 z^2 - 125707982400 z^3 + 48886437600 z^4 + 31998395520 z^5 + 6837264000 z^6 + 729308160 z^7 + 41368320 z^8 + 1182720 z^9 + 13312 z^10) Erf[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},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},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]