Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alki)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.alki.01

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(11/2), 3}, z] == (1/147349125) (4 E^(z/2) (44438625 - 59875200 z + 50859900 z^2 - 39690000 z^3 + 34927200 z^4 - 43545600 z^5 + 141039360 z^6 + 384998400 z^7 + 212716800 z^8 + 47308800 z^9 + 4899840 z^10 + 233472 z^11 + 4096 z^12) BesselI[0, z/2]) + (1/(147349125 z)) (4 E^(z/2) (-30405375 - 6081075 z + 30447900 z^2 - 30221100 z^3 + 23814000 z^4 - 19504800 z^5 + 20079360 z^6 - 34041600 z^7 + 230273280 z^8 + 172089600 z^9 + 42746880 z^10 + 4672512 z^11 + 229376 z^12 + 4096 z^13) BesselI[1, z/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},{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]