Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8sc)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8sc.01

Input Form

HypergeometricPFQ[{-(13/4)}, {11/2, 11/4}, z] == -((1/(878938030080 z^(9/2))) ((7 (4 (619164000 + 1238328000 Sqrt[z] + 454896000 z - 741312000 z^(3/2) + 256089600 z^2 + 1940889600 z^(5/2) - 68190525 z^3 + 3263703300 z^(7/2) + 1595168640 z^4 - 7032426240 z^(9/2) - 243202560 z^5 + 996710400 z^(11/2) + 8192000 z^6 - 32964608 z^(13/2) - 65536 z^7 + 262144 z^(15/2) + E^(4 Sqrt[z]) (-619164000 + 1238328000 Sqrt[z] - 454896000 z - 741312000 z^(3/2) - 256089600 z^2 + 1940889600 z^(5/2) + 68190525 z^3 + 3263703300 z^(7/2) - 1595168640 z^4 - 7032426240 z^(9/2) + 243202560 z^5 + 996710400 z^(11/2) - 8192000 z^6 - 32964608 z^(13/2) + 65536 z^7 + 262144 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (9628868925 + 17117989200 z - 28830297600 z^2 + 4011171840 z^3 - 132055040 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (9628868925 + 17117989200 z - 28830297600 z^2 + 4011171840 z^3 - 132055040 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])))

Standard Form

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MathML 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]