Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8415)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8415.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 13/4}, -z] == (Sqrt[Pi] z^(1/4) (37829509383290625 - 193687088042448000 z + 1205164103375232000 z^2 + 988852597641216000 z^3 + 166193713889280000 z^4 + 9209002328064000 z^5 + 196458716332032 z^6 + 1629940088832 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-13822592969441025 + 41983233407161200 z + 53834957808065280 z^2 + 9889622911365120 z^3 + 564418584576000 z^4 + 12184156372992 z^5 + 101619597312 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + 4 (3000864551731200 - 15398232688394325 z + 66855520158966000 z^2 + 60063597324783360 z^3 + 10283975064760320 z^4 + 573301496807424 z^5 + 12259679010816 z^6 + 101820923904 z^7 + 268435456 z^8) Sin[2 Sqrt[z]]))/ (1251851124709785600 z^(5/2))

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]